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BEGIN:VEVENT
SUMMARY:Romain Aimino (University of Porto)
DTSTART;VALUE=DATE-TIME:20201113T140000Z
DTEND;VALUE=DATE-TIME:20201113T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/1
DESCRIPTION:Title: Large deviations estimates for dynamical systems with stretched expo
nential decay of correlations\nby Romain Aimino (University of Porto)
as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nDuring thi
s talk\, I will discuss results on large deviations estimates for dynamica
l systems with stretched exponential decay of correlations. This class of
systems encompasses for instance Viana maps and intermittent maps exhibiti
ng a stretched exponential fast accumulation of pre-orbits at 0. Optimal r
ates for large deviations of such systems are still unknown. I will presen
t a substancial improvement obtained in a joint work with Jorge Freitas.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeor Hafouta (Ohio State University)
DTSTART;VALUE=DATE-TIME:20201120T140000Z
DTEND;VALUE=DATE-TIME:20201120T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/2
DESCRIPTION:Title: Limit theorems for some time-dependent expanding dynamical systems\nby Yeor Hafouta (Ohio State University) as part of Zoominar in Dynamic
al Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Matheus (Centre de Mathématiques Laurent Schwartz)
DTSTART;VALUE=DATE-TIME:20201127T140000Z
DTEND;VALUE=DATE-TIME:20201127T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/3
DESCRIPTION:Title: Speed of mixing of geodesic flows on certain non-positively curved s
urfaces\nby Carlos Matheus (Centre de Mathématiques Laurent Schwartz)
as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nIn this t
alk\, we discuss the speed of mixing on certain surfaces whose curvatures
are negative except along a closed geodesic. This is a joint work in progr
ess with Y. Lima and I. Melbourne\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaqueline Siqueira (Universidade Federal do Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20201204T140000Z
DTEND;VALUE=DATE-TIME:20201204T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/4
DESCRIPTION:Title: Equilibrium states for a class of non-uniformly hyperbolic maps\
nby Jaqueline Siqueira (Universidade Federal do Rio de Janeiro) as part of
Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe consider a wide f
amily of non-uniformly hyperbolic maps and hyperbolic potentials and prove
that the unique equilibrium state associated to each element of the famil
y is given by the eigenmeasure and the eigenfunction of the transfer opera
tor (both having the spectral radius as an eigenvalue). We prove that the
transfer operator has the spectral gap property in the space of Hölder c
ontinuous observables. From this we derive that the unique equilibrium sta
te satisfies a central limit theorem and that it has exponential decay of
correlations. Moreover\, we prove joint continuity and analyticity with re
spect to the potential. (Based on various joint works with S. Afonso\, J.
Alves\, V. Ramos.)\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201218T140000Z
DTEND;VALUE=DATE-TIME:20201218T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/6
DESCRIPTION:Title: Central limit theorems for counting measures in coarse negative curv
ature\nby Giulio Tiozzo (University of Toronto) as part of Zoominar in
Dynamical Systems @ Porto\n\n\nAbstract\nWe establish general central lim
it theorems for an action of a group on a hyperbolic space with respect to
counting for the word length in the group. In 2013\, Chas\, Li\, and Mask
it produced numerical experiments on random closed geodesics on a hyperbol
ic pair of pants. Namely\, they drew uniformly at random conjugacy classes
of a given word length\, and considered the hyperbolic length of the corr
esponding closed geodesic on the pair of pants. Their experiments lead to
the conjecture that the length of these closed geodesics satisfies a cent
ral limit theorem\, and we proved this conjecture in 2018. In our new work
\, we remove the assumptions of properness and smoothness of the space\, o
r cocompactness of the action\, thus proving a general central limit theor
em for group actions on hyperbolic spaces. We will see how our techniques
replace the classical thermodynamic formalism and allow us to provide new
applications\, including to lengths of geodesics in geometrically finite m
anifolds and to intersection numbers with submanifolds. Joint work with I.
Gekhtman and S. Taylor.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong-Kun Zhang (University of Massachusetts Amherst)
DTSTART;VALUE=DATE-TIME:20210115T140000Z
DTEND;VALUE=DATE-TIME:20210115T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/7
DESCRIPTION:Title: Levy diffusion for Lorentz gas with flat points\nby Hong-Kun Zha
ng (University of Massachusetts Amherst) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe investigate the diffusion and statistic
al properties of Lorentz gas with cusps at flat points. The underlying d
ynamical systems are modifications of dispersing billiards with cusps.
The systems generate stochastic processes with slow mixing rates of orde
r $n^{-a$}\, for $ a\\in (0\,1)$. We are able to show that these stocha
stic processes enjoy stable law and have super-diffusion driven by Lev
y processes.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jairo Bochi (PUC Santiago de Chile)
DTSTART;VALUE=DATE-TIME:20210122T140000Z
DTEND;VALUE=DATE-TIME:20210122T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/8
DESCRIPTION:Title: Topological emergence\nby Jairo Bochi (PUC Santiago de Chile) as
part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nI will expla
in the notion of topological emergence of a dynamical system\, introduced
by Pierre Berger and myself (2019). Topological emergence is a measurement
of diversity of statistical behavior\, and it is independent of the tradi
tional notions of dynamical complexity\, such as entropy. I will show an u
niversal bound on topological emergence depending on the ambient dimension
\, and I will discuss the problem of computing topological emergence of so
me hyperbolic dynamical systems. I will sketch the proofs.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Cristina Freitas (University of Porto)
DTSTART;VALUE=DATE-TIME:20210129T140000Z
DTEND;VALUE=DATE-TIME:20210129T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/9
DESCRIPTION:Title: The cluster size distribution and the extremal index\nby Ana Cri
stina Freitas (University of Porto) as part of Zoominar in Dynamical Syste
ms @ Porto\n\n\nAbstract\nThe extremal index appears as a parameter in Ext
reme Value Laws for stochastic processes\, characterising the clustering o
f extreme events. We apply this idea in a dynamical systems context to ana
lyse the possible Extreme Value Laws for the stochastic process generated
by observations taken along dynamical orbits. In this context\, the existe
nce of an extremal index less than 1 is associated to the occurrence of pe
riodic phenomena. For generic points\, the exceedances\, in the limit\, ar
e singular and occur at Poisson times. However\, around periodic points\,
the picture is different: the respective point processes of exceedances co
nverge to a compound Poisson process\, so instead of single exceedances\,
we have entire clusters of exceedances occurring at Poisson times with a g
eometric distribution ruling its multiplicity. The extremal index usually
coincides with the reciprocal of the mean of the limiting cluster size dis
tribution. Here\, we build dynamically generated stochastic processes with
an extremal index for which that equality does not hold. The mechanism we
use is based on considering observable functions maximized at at least tw
o points of the phase space\, where one of them is an indifferent periodic
point. For the second point at which the observable function is maximized
we consider either a periodic or a nonperiodic point. We explore two such
examples and\, for each of them\, we compute the extremal index and prese
nt the corresponding cluster size distribution.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugen Mihailescu (IRMAR)
DTSTART;VALUE=DATE-TIME:20210205T140000Z
DTEND;VALUE=DATE-TIME:20210205T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/10
DESCRIPTION:Title: Dynamics for a class of skew-product endomorphisms and applications
\nby Eugen Mihailescu (IRMAR) as part of Zoominar in Dynamical Systems
@ Porto\n\n\nAbstract\nI will present a new notion of Smale endomorphisms
and the skew-products coded by them. Equilibrium measures are studied for
these piecewise smooth transformations\; their projections are shown to b
e exact dimensional in fibers and globally\, and dimension formulas are ob
tained. This applies to skew-products over EMR maps and natural extensions
. Then we extend the Doeblin-Lenstra Conjecture on Diophantine approximati
on coefficients for a larger class of measures and of irrational numbers.
Another application is to a type of complex continued fractions with compl
ex digits. Based on joint work with M. Urbanski.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Jurga (University of St Andrews)
DTSTART;VALUE=DATE-TIME:20210212T140000Z
DTEND;VALUE=DATE-TIME:20210212T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/11
DESCRIPTION:Title: Box dimensions of $(\\times m\, \\times n)$ invariant sets\nby
Natalia Jurga (University of St Andrews) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe study the box dimensions of sets which a
re invariant under the toral endormorphism $(x\, y) \\mapsto (m x \\mod 1
\, n y \\mod 1)$ for integers $n>m \\geq 2$. This is a fundamental exampl
e of an expanding\, nonconformal dynamical system\, and invariant sets hav
e many subtle properties. The basic examples of such invariant sets are Be
dford-McMullen carpets and\, more generally\, invariant sets are modelled
by subshifts on the associated symbolic space. When this subshift is topol
ogically mixing and sofic\, the situation is well-understood by results of
Kenyon and Peres\, in particular the box dimension satisfies a natural fo
rmula in terms of entropy and the expansion coefficients $m\,n$. In this
talk we will discuss what happens beyond the sofic and mixing case\, which
is partly based on joint work with Jonathan Fraser (St Andrews).\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Kloeckner (Université Paris-Est)
DTSTART;VALUE=DATE-TIME:20210219T140000Z
DTEND;VALUE=DATE-TIME:20210219T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/12
DESCRIPTION:Title: Effective high-temperature estimates ensuring a spectral gap\nb
y Benoît Kloeckner (Université Paris-Est) as part of Zoominar in Dynamic
al Systems @ Porto\n\n\nAbstract\nThe main goal of the talk shall be to ex
plain a few ideas from two classical theories : the thermodynamical formal
ism\, and the perturbation of linear operators. The "thermodynamical forma
lism" is a framework to describe particular invariant measures of dynamica
l systems\, called "equilibrium states"\, parametrized by functions on the
phase space\, called "potentials". This formalism is based on the "transf
er operator"\; when this operator has a spectral gap\, the equilibrium sta
te exists\, is unique\, and has very good statistical properties (exponent
ial mixing\, Central Limit Theorem\, etc.) If one perturbs slightly the po
tential\, the corresponding transfer operator is also perturbed. The class
ical theory of perturbation of operators ensures that the spectral gap pro
perty is an open condition and that under bounded pertubration\, the eigen
data of an operator depends analytically on the perturbation. It turns out
that using the Implicit Function Theorem\, this theory can be made effect
ive with explicit bounds on the size of a neighborhood where the spectral
gap persists. Using this effective perturbation theory\, we show completel
y explicit bound on the potential ensuring the spectral gap property for t
ransfer operators of classical families of dynamical systems.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Rodriguez-Hertz (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20210226T140000Z
DTEND;VALUE=DATE-TIME:20210226T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/13
DESCRIPTION:Title: Rigidity for expanding maps\nby Federico Rodriguez-Hertz (Penns
ylvania State University) as part of Zoominar in Dynamical Systems @ Porto
\n\n\nAbstract\nIn this talk I will discuss a plan started joint with A. G
ogolev to find rigidity property in hyperbolic dynamics. This plan focuses
on matching of smooth potentials for different dynamics. I will present a
successful instance of this plan in the setting of expanding maps.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Shinoda (Keio University)
DTSTART;VALUE=DATE-TIME:20210305T130000Z
DTEND;VALUE=DATE-TIME:20210305T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/14
DESCRIPTION:Title: Non-convergence of equilibrium states at zero temperature limit
\nby Mao Shinoda (Keio University) as part of Zoominar in Dynamical System
s @ Porto\n\n\nAbstract\nWe construct finite-range interactions on a two d
imensional symbolic dynamical system\, for which the associated equilibriu
m states (i.e.\, the shift-invariant Gibbs states) fail to converge as tem
perature goes to zero. More precisely\, if we pick any one-parameter famil
y of equilibrium states at inverse temperature for this interaction\, then
the limit does not exist. This settles a question posed by Chazottes and
Hochman who obtained such a non-convergence behavior when dimension greate
r than 3.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerôme Buzzi (Université de Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210312T140000Z
DTEND;VALUE=DATE-TIME:20210312T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/15
DESCRIPTION:Title: Continuity of Lyapunov exponents for surface diffeomorphisms\nb
y Jerôme Buzzi (Université de Paris-Saclay) as part of Zoominar in Dynam
ical Systems @ Porto\n\n\nAbstract\nIn the setting of smooth surface diffe
omorphisms\, we show that the lower semicontinuity defect of the exponents
bounds that of the entropy. In particular\, Hausdorff dimension is upper
semicontinuous among ergodic invariant probability measures with entropy b
ounded away from zero. We also obtain a new criterion for the existence of
an SRB measure with positive entropy. Joint work with Sylvain CROVISIER a
nd Omri SARIG.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Lima (Federal University of Ceará)
DTSTART;VALUE=DATE-TIME:20210319T140000Z
DTEND;VALUE=DATE-TIME:20210319T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/16
DESCRIPTION:Title: Symbolic dynamics for maps with high dimension\nby Yuri Lima (F
ederal University of Ceará) as part of Zoominar in Dynamical Systems @ Po
rto\n\n\nAbstract\nWe construct Markov partitions for non-invertible and/o
r singular nonuniformy hyperbolic systems defined on higher dimensional R
iemannian manifolds. The gen- erality of the setup covers classical exampl
es not treated so far\, such as geodesic flows in closed manifolds\, mult
idimensional billiard maps\, and Viana maps\, as well as includes all the
recent results of the literature. We also provide a wealth of applications
. Joint work with Ermerson Araujo and Mauricio Poletti.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bálasz Bárány (Budapest University of Technology and Economics)
DTSTART;VALUE=DATE-TIME:20210326T140000Z
DTEND;VALUE=DATE-TIME:20210326T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/17
DESCRIPTION:Title: On the convergence rate of the chaos game\nby Bálasz Bárány
(Budapest University of Technology and Economics) as part of Zoominar in D
ynamical Systems @ Porto\n\n\nAbstract\nIn the 1988 textbook "Fractals Eve
rywhere" M. Barnsley introduced an algorithm for generating fractals throu
gh a random procedure which he called the chaos game. In this talk we show
how long it takes the orbit of the chaos game to reach a certain density
inside the attractor of a strictly contracting iterated function system of
which we only assume that its lower dimension is positive. We show that t
he rate of growth of this cover time is determined by the Minkowski dimens
ion of the push-forward of the shift invariant measure with exponential de
cay of correlations driving the chaos game. As an application\, for Bedfor
d-McMullen carpets we completely characterise the family of probability ve
ctors which minimise the Minkowski dimension of Bernoulli measures. Intere
stingly\, these vectors have not appeared in any other aspect of Bedford-M
cMullen carpets before. This is a joint work with Natalia Jurga and Istvá
n Kolossváry.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Carvalho (University of Porto)
DTSTART;VALUE=DATE-TIME:20210409T130000Z
DTEND;VALUE=DATE-TIME:20210409T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/18
DESCRIPTION:Title: Generalized entropy functions\, variational principles and equilibr
ium states\nby Maria Carvalho (University of Porto) as part of Zoomina
r in Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Froyland (University of New South Wales)
DTSTART;VALUE=DATE-TIME:20210416T090000Z
DTEND;VALUE=DATE-TIME:20210416T100000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/19
DESCRIPTION:Title: Stability and approximation of statistical limit laws\nby Gary
Froyland (University of New South Wales) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nThe unpredictability of chaotic nonlinear d
ynamics leads naturally to statistical descriptions\, including probabilis
tic limit laws such as the central limit theorem and large deviation princ
iple. A key tool in the Nagaev-Guivarc'h spectral method for establishing
statistical limit theorems is a "twisted" transfer operator. We prove stab
ility of the variance in the central limit theorem and the rate function f
rom a large deviation principle with respect to deterministic and stochast
ic perturbations of the dynamics and perturbations induced by numerical sc
hemes. We then apply these results to piecewise expanding maps in one and
multiple dimensions. This theory can be extended to uniformly hyperbolic m
aps and in this setting we develop two new Fourier-analytic methods to pro
vide the first rigorous estimates of the variance and rate function for An
osov maps. This is joint work with Harry Crimmins.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaughn Climenhaga (University of Houston)
DTSTART;VALUE=DATE-TIME:20210430T130000Z
DTEND;VALUE=DATE-TIME:20210430T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/20
DESCRIPTION:Title: Counting closed geodesics on surfaces without conjugate points\
nby Vaughn Climenhaga (University of Houston) as part of Zoominar in Dynam
ical Systems @ Porto\n\n\nAbstract\nFor negatively curved Riemannian manif
olds\, Margulis gave an asymptotic formula for the number of closed geodes
ics with length below a given threshold. I will describe joint work with G
erhard Knieper and Khadim War in which we obtain the corresponding result
for surfaces without conjugate points by first proving uniqueness of the m
easure of maximal entropy and then following the approach of recent work b
y Russell Ricks\, who established the asymptotic estimates in the setting
of CAT(0) geodesic flows.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Oprocha (University of Science and Technology\, Krakow)
DTSTART;VALUE=DATE-TIME:20210423T130000Z
DTEND;VALUE=DATE-TIME:20210423T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/21
DESCRIPTION:Title: On the dynamics of Lorenz maps\nby Piotr Oprocha (University of
Science and Technology\, Krakow) as part of Zoominar in Dynamical Systems
@ Porto\n\n\nAbstract\nIn this talk we will present several dynamical pro
perties of expanding Lorenz maps\, which roughly speaking are increasing i
nterval maps with one point of discontinuity. We will put special emphasis
on piecewise linear case: x -> beta x + alpha (mod 1) Among other\, we
will consider such properties as transitivity\, mixing\, renormalizations\
, minimal cycles and proper invariant sets.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polina Vytnova (University of Warwick)
DTSTART;VALUE=DATE-TIME:20210514T130000Z
DTEND;VALUE=DATE-TIME:20210514T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/22
DESCRIPTION:Title: Computing Hausdorff dimension of Bernoulli convolutions\nby Pol
ina Vytnova (University of Warwick) as part of Zoominar in Dynamical Syste
ms @ Porto\n\n\nAbstract\nIt is well known that for any 0~~1/2 is very intricate and has been a subject of intensive research
which dates back to Erdos. To date\, it is not known whether or not the me
asure is singular or absolutely continuous for a given s. The problem of c
omputing the Hausdorff dimension of the measure is also open in general\,
though there have been several major advances in recent years. \n In the t
alk I will discuss a new approach to uniform lower bounds on Hausdorff dim
ension of Bernoulli convolution measures\, based on random dynamics.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART;VALUE=DATE-TIME:20210521T130000Z
DTEND;VALUE=DATE-TIME:20210521T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/23
DESCRIPTION:Title: Thermodynamic formalism for coarse expanding dynamical systems\
nby Tushar Das (University of Wisconsin - La Crosse) as part of Zoominar i
n Dynamical Systems @ Porto\n\n\nAbstract\nWe report on a joint project (h
ttps://arxiv.org/abs/1908.08270 or https://doi.org/10.1007/s00220-021-0405
8-2) with Giulio Tiozzo\, Feliks Przytycki\, Mariusz Urbanski\, and Anna Z
dunik that develops the thermodynamic formalism for weakly coarse expandin
g dynamical systems (finite branched covers of locally connected spaces th
at possess some expansion). There are no assumptions of finiteness of the
postcritical set\, conformality\, holomorphy\, or smoothness in this setti
ng. After encoding the dynamics via geometric code trees\, our stochastic
laws follow from those for the shift dynamics on the associated code space
. The area is in its nascency and there are plenty of open problems and di
rections that await exploration.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Shmerkin (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210528T150000Z
DTEND;VALUE=DATE-TIME:20210528T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/24
DESCRIPTION:Title: Beyond Furstenberg's intersection conjecture\nby Pablo Shmerkin
(University of British Columbia) as part of Zoominar in Dynamical Systems
@ Porto\n\n\nAbstract\nHillel Furstenberg conjectured in the 1960s that t
he intersections of closed ×2 and ×3-invariant Cantor sets have “small
” Hausdorff dimension. This conjecture was proved independently by Meng
Wu and by myself\; recently\, Tim Austin found a simple proof. I will pres
ent some generalizations of the intersection conjecture and other related
results.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Kryzhevich (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20210507T130000Z
DTEND;VALUE=DATE-TIME:20210507T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/25
DESCRIPTION:Title: Interval translation maps\, their invariant measures and their prop
erties\nby Sergey Kryzhevich (Saint Petersburg State University) as pa
rt of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe study proper
ties of the so-called interval translation maps (ITMs). Informally\, we co
nsider interval exchange maps with overlaps. A survey on the recent develo
pments in this area will be given with some author’s results being menti
oned. For example\, we prove that any ITM admits a Borel probability non-a
tomic invariant measure. We introduce the so-called maximal invariant meas
ure that is the measure supported on the largest possible set. It will be
demonstrated that any ITM\, endowed with this measure\, is isomorphic to a
n interval exchange map. This will imply various corollaries: the estim
ate on the maximal number of non-atomic ergodic invariant measures\, minim
ality if the symbolic model\, unique ergodicity\, ‘closing lemma’\, et
c. Besides\, we discuss the problem of robustness of invariant measures wi
th respect to small perturbations of the parameters of the system. Finall
y\, a real-life model of risk management will be considered. We demonstrat
e that this model can be reduced to an ITM and study the properties of the
obtained map.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dalia Terhesiu (University of Leiden)
DTSTART;VALUE=DATE-TIME:20210604T130000Z
DTEND;VALUE=DATE-TIME:20210604T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/26
DESCRIPTION:Title: Lorentz gases with small scatterers\nby Dalia Terhesiu (Univers
ity of Leiden) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstr
act\nWe study Lorentz gases with scatterer size going to zero. In work in
progress with Balint and Bruin\, we obtain a precise understanding of the
allowed path of taking limits as the size of the scatterers goes to zero
and time goes to infinity so that the Central Limit Law (with non-standard
normalization) persists. This type of joint law is in the gist of Boltzma
nn–Grad limit. Further we obtain joint local limit theorems and mixing a
s the size of the scatterers goes to zero and time goes to infinity.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Sadovskaya (Penn State University)
DTSTART;VALUE=DATE-TIME:20210611T130000Z
DTEND;VALUE=DATE-TIME:20210611T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/27
DESCRIPTION:Title: Diffeomorphism cocycles over partially hyperbolic systems\nby V
ictoria Sadovskaya (Penn State University) as part of Zoominar in Dynamica
l Systems @ Porto\n\n\nAbstract\nWe consider cocycles over an accessible p
artially hyperbolic system with values in the group of diffeomorphisms of
a compact manifold M. We will discuss the following results for this setti
ng: existence of a continuous invariant family of Riemannian metrics on M
for a bounded cocycle\, continuity of a measurable conjugacy between two c
ocycles\, and a sufficient condition for existence of a continuous conjuga
cy.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vilton Pinheiro (Federal University of Bahia)
DTSTART;VALUE=DATE-TIME:20210618T130000Z
DTEND;VALUE=DATE-TIME:20210618T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/28
DESCRIPTION:Title: Ergodic formalism and topological attractors\nby Vilton Pinheir
o (Federal University of Bahia) as part of Zoominar in Dynamical Systems @
Porto\n\n\nAbstract\nWe introduce the concept of Baire Ergodicity and Erg
odic Formalism. Using them to study topological and statistical attractors
\, we give several applications for maps of the interval\, expanding and p
artially hyperbolic maps\, strongly dissipative dynamics and skew-products
. In dynamical systems with abundance of historical behavior (and this in
cludes all systems with some hyperbolicity\, in particular\, Axiom A syste
ms)\, we cannot use an invariant probability to control the asymptotic top
ological/statistical behavior of a generic orbit\, except when it belongs
to the basin of a periodic orbit of attraction. However\, Baire's Ergodici
ty and Ergodic Formalism can also be applied in this context\, contributin
g to the study of generic orbits of systems with an abundance of historica
l behavior.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davor Dragičević (University of Rijeka)
DTSTART;VALUE=DATE-TIME:20210702T130000Z
DTEND;VALUE=DATE-TIME:20210702T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/29
DESCRIPTION:Title: Quenched limit theorems for expanding on average cocycles\nby D
avor Dragičević (University of Rijeka) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nIn [1\, 2]\, the authors extended the class
ical spectral method for establishing limit theorems for deterministic dyn
amical systems to random piecewise-expanding and hyperbolic dynamical syst
ems exhibiting uniform decay of correlations. In this talk we will discuss
a certain modification of this method that enables us to establish limit
theorems for a class of random piecewise expanding dynamics that doesn't e
xhibit uniform decay of correlations. This is a joint work with Julien Sed
ro [3].\n \n[1] D. Dragičević et. al. A spectral approach for quenched
limit theorems for random expanding dynamical systems\, Comm. Math. Phys.
360 (2018)\, 1121--1187. \n[2] D. Dragičević et. al. A spectral approach
for quenched limit theorems for random hyperbolic dynamical systems\, Tra
ns. Amer. Math. Soc. 373 (2020)\, 629--664. \n[3] D. Dragičević and J. S
edro\, Quenched limit theorems for expanding on average cocycles\, preprin
t (2021)\, https://arxiv.org/abs/2105.00548\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafael Potrie (Universidad de la Republica)
DTSTART;VALUE=DATE-TIME:20210709T130000Z
DTEND;VALUE=DATE-TIME:20210709T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/30
DESCRIPTION:Title: Ergodicity of a class of partially hyperbolic systems\nby Rafae
l Potrie (Universidad de la Republica) as part of Zoominar in Dynamical Sy
stems @ Porto\n\n\nAbstract\nWe study the problem of determining when a pa
rtially hyperbolic diffeomorphism in dimension 3 is ergodic without need f
or perturbations. We show that for a large class of such systems\, that we
called collapsed Anosov flows and which cover full connected components o
f partially hyperbolic systems we have ergodicity unless there is a torus
tangent to the $su$-direction which is known to impose strong conditions o
n the topology of the underlying manifold. I will try to explain the conte
xt of this result\, and hopefully be able to provide some taste of the pro
ofs. This is joint work with S. Fenley.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerôme Rousseau (Federal University of Bahia & University of Port
o)
DTSTART;VALUE=DATE-TIME:20210709T140000Z
DTEND;VALUE=DATE-TIME:20210709T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/31
DESCRIPTION:Title: Longest common substring for random subshifts of finite type\nb
y Jerôme Rousseau (Federal University of Bahia & University of Porto) as
part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe study the
behaviour of the longest common substring for random subshifts of finite t
ype. We prove that\, under some exponential mixing assumptions\, this beha
viour is linked to the Rényi entropy. We will show quenched and annealed
results. In particular\, we will see that in the quenched case we obtain a
phase transition which does not appear in the annealed case. This talk in
cludes some joint works with Adriana Coutinho\, Rodrigo Lambert\, Sébasti
en Gouezel and Manuel Stadlbauer.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Rivera-Letelier (University of Rochester)
DTSTART;VALUE=DATE-TIME:20210709T150000Z
DTEND;VALUE=DATE-TIME:20210709T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/32
DESCRIPTION:Title: Prime orbit counting for Collet-Eckmann maps\nby Juan Rivera-Le
telier (University of Rochester) as part of Zoominar in Dynamical Systems
@ Porto\n\n\nAbstract\nA discussion of prime orbit counting results for re
al and complex maps\, where periodic orbits are weighted according to thei
r Lyapunov exponents. For real and complex maps satisfying the Collet-Eckm
ann condition\, we obtain a result with a power savings error term. In com
parison with the hyperbolic case\, the main technical difficulty stems fro
m the relatively wild geometric properties of the absolutely continuous in
variant measure. This is a joint work with Li Zhiqiang.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Crovisier (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210910T130000Z
DTEND;VALUE=DATE-TIME:20210910T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/33
DESCRIPTION:Title: Strong positive recurrence for surface diffeomorphisms\nby Sylv
ain Crovisier (Université Paris-Saclay) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe introduce the strong positive recurrence
property for diffeomorphisms of a manifold and show that it holds for eve
ry C-infinity surface diffeomorphism with positive topological entropy. It
implies that the ergodic measures maximizing the entropy have exponential
decay of correlations and satisfy a central limit theorem. This is a join
t work with J. Buzzi and O. Sarig.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Godofredo Iommi (PUC - Chile)
DTSTART;VALUE=DATE-TIME:20210910T140000Z
DTEND;VALUE=DATE-TIME:20210910T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/34
DESCRIPTION:Title: An ergodic theorem for symmetric averages\nby Godofredo Iommi (
PUC - Chile) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstrac
t\nWe introduce a notion of barycenter of a probability measure related to
the symmetric mean of a collection of nonnegative real numbers. Our defin
ition is inspired by the work of Halász and Székely\, who in 1976 proved
a law of large numbers for symmetric means. We establish fundamental ineq
ualities that relate the symmetric mean of a list of nonnegative real numb
ers with the barycenter of the measure uniformly supported on these points
. As a consequence\, we go on to establish an ergodic theorem stating that
the symmetric means of a sequence of dynamical observations converges to
the Halász-Székely barycenter of the corresponding distribution. This is
joint work with Jairo Bochi and Mario Ponce.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenichiro Yamamoto (Nagaoka University)
DTSTART;VALUE=DATE-TIME:20210924T130000Z
DTEND;VALUE=DATE-TIME:20210924T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/35
DESCRIPTION:Title: Large deviation principle for piecewise monotonic maps with density
of periodic measures\nby Kenichiro Yamamoto (Nagaoka University) as p
art of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe show that a
piecewise monotonic map with positive topological entropy satisfies the l
evel-2 large deviation principle with a unique measure of maximal entropy
as reference under the conditions that the corresponding Markov diagram is
irreducible and that the periodic measures of the map are dense in the se
t of ergodic measures. This result can apply to a broad class of piecewise
monotonicmaps\, such as monotonic mod one transformations and piecewise m
onotonic maps with two monotonic pieces.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Darji (University of Louisville)
DTSTART;VALUE=DATE-TIME:20210924T140000Z
DTEND;VALUE=DATE-TIME:20210924T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/36
DESCRIPTION:Title: Generalized Hyperbolicity and the Shadowing Property in Linear Dyna
mics\nby Dario Darji (University of Louisville) as part of Zoominar in
Dynamical Systems @ Porto\n\n\nAbstract\nIn this talk we discuss recent r
esults and open questions concerning in Hyperbolicity\, Generalized Hype
rbolicity and the Shadowing Property in the setting of linear dynamics. In
particular\, we discuss some results concerning when the Generalized Hype
rbolicity is equivalent to the Shadowing Property. This talk will be acces
sible to grad students and non-specialists. All notions and background mat
erial will be clearly explained.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catalina Freijo (University of Lisbon)
DTSTART;VALUE=DATE-TIME:20211008T130000Z
DTEND;VALUE=DATE-TIME:20211008T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/37
DESCRIPTION:Title: Lyapunov exponents for non-uniformly fiber bunched linear cocycles<
/a>\nby Catalina Freijo (University of Lisbon) as part of Zoominar in Dyna
mical Systems @ Porto\n\n\nAbstract\nWe consider a fixed hyperbolic dynami
cs in the base and perturb the cocycle for studying the continuity of Lyap
unov exponents. For the case of uniformly fiber bunched cocycles\, continu
ity was proved by Backes\, Brown and Butler. In this work we present a cha
racterization for continuity in the case of non-uniformly fiber bunched dy
namics which is a partial answer to the conjecture of Marcelo Viana. This
is a joint work with Karina Marin (UFMG).\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvius Klein (PUC-Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20211008T140000Z
DTEND;VALUE=DATE-TIME:20211008T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/38
DESCRIPTION:Title: Mixed random-quasiperiodic cocycles\nby Silvius Klein (PUC-Rio
de Janeiro) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract
\nThe purpose of this talk is to introduce the concept of mixed random-qua
siperiodic linear cocycles and to discuss the ergodicity of its base dynam
ics as well as the positivity and continuity of the corresponding Lyapuno
v exponent. This is part of a larger joint project with Ao Cai and Pedro D
uarte (both from the University of Lisbon) whose aim is to study the stabi
lity under random perturbations of certain quasiperiodic systems.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Tahzibi (University of São Paulo - ICMC)
DTSTART;VALUE=DATE-TIME:20211022T130000Z
DTEND;VALUE=DATE-TIME:20211022T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/39
DESCRIPTION:Title: Equilibrium states for discretized Anosov flows\nby Ali Tahzibi
(University of São Paulo - ICMC) as part of Zoominar in Dynamical System
s @ Porto\n\n\nAbstract\nWe consider partially hyperbolic diffeomorphisms
which appeared in the classification of partially hyperbolic diffeomorphis
ms homotopic to identity on three-manifolds. In a previous result with Buz
zi and Fisher we constructed measures of maximal entropy for such diffeomo
rphisms and later proved some rigidity result about such measures joint wi
th Buzzi-Crovisier-Poletti. In this talk we announce also some existence/c
onstruction results and discuss uniqueness of (u-)equilibrium states in t
his setting in a work that is essentially part of the thesis of my student
Richard Becerra.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kucherenko (CCNY)
DTSTART;VALUE=DATE-TIME:20211022T140000Z
DTEND;VALUE=DATE-TIME:20211022T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/40
DESCRIPTION:Title: Flexibility of the Pressure Function\nby Tamara Kucherenko (CCN
Y) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe disc
uss the flexibility of the pressure function of a continuous potential (ob
servable) with respect to a parameter regarded as the inverse temperature.
The points of non-differentiability of this function are of particular in
terest in statistical physics\, since they correspond to phase transitions
. It is well known that the pressure function is convex\, Lipschitz\, and
has an asymptote at infinity. We prove that in a setting of one-dimensiona
l compact symbolic systems these are the only restrictions. We present a m
ethod to explicitly construct a continuous potential whose pressure functi
on coincides with any prescribed convex Lipschitz asymptotically linear fu
nction starting at a given positive value of the parameter. As a conseque
nce\, we obtain that for a continuous observable the phase transitions ca
n occur at a countable dense set of temperature values. We go further and
show that one can vary the cardinality of the set of ergodic equilibrium
states as a function of the parameter to be any number\, finite or infini
te. This is based on joint work with Anthony Quas.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Lukina (University of Vienna)
DTSTART;VALUE=DATE-TIME:20211105T140000Z
DTEND;VALUE=DATE-TIME:20211105T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/41
DESCRIPTION:Title: Weyl groups and the growth of cycles in actions on rooted trees
\nby Olga Lukina (University of Vienna) as part of Zoominar in Dynamical S
ystems @ Porto\n\n\nAbstract\nMaximal tori and Weyl groups play an importa
nt role in the study of compact connected Lie groups. In this talk\, we in
troduce an analogous notion for profinite groups acting on rooted trees. W
e then use Weyl groups to study the conjecture by Boston and Jones\, that
settled elements are dense in the images of representations of absolute Ga
lois groups of number fields into automorphism groups of rooted trees. An
element is settled if it satisfies certain conditions on the growth of cyc
les in its restrictions to finite levels of the tree. This is joint work w
ith Maria Isabel Cortez.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Carrasco (Federal University of Minas Gerais)
DTSTART;VALUE=DATE-TIME:20211105T150000Z
DTEND;VALUE=DATE-TIME:20211105T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/42
DESCRIPTION:Title: Non-uniformly hyperbolic endomorphisms\nby Pablo Carrasco (Fede
ral University of Minas Gerais) as part of Zoominar in Dynamical Systems @
Porto\n\n\nAbstract\nConsider an endomorphism E of the 2-dimensional toru
s (a matrix with integer coefficients and determinant equal to one) and su
ppose that it is not a multiple of the identity. Then there exists an endo
morphism homotopic to E that is area preserving and which is robustly (C1!
) non-uniformly hyperbolic\; it has one positive and one negative Lyapunov
exponent\, almost everywhere with respect to Lebesgue. This result is pa
rt of a joint work with Martin Andersson (UFF) and Radu Saghin (PUCV).\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Panti (University of Udine)
DTSTART;VALUE=DATE-TIME:20211119T140000Z
DTEND;VALUE=DATE-TIME:20211119T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/43
DESCRIPTION:Title: Attractors of dual continued fractions\nby Giovanni Panti (Univ
ersity of Udine) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbs
tract\nWe identify continued fractions with piecewise-projective Markov ma
ps on some interval\, provided that all branches are induced by elements i
n a fixed Hecke triangle group. Ordinary continued fractions constitute a
very special case\, relative to the (2\,3\,infinity) group. The branches o
f the map are expanding on the domain interval\, but contracting on some o
ther part of the real projective line. As such\, they give rise to an IFS
whose attractor is relevant\, since it determines the natural extension an
d several properties\, both algebraic and dynamical\, of the original syst
em. We use an appropriate generalization of the classical Minkowski Questi
on Mark function to simultaneously linearize all maps resulting from the s
ame triangle group\, and to prove that the above IFS satisfies the open se
t condition. We draw consequences -as well as open problems- from these fa
cts.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Sedro (LPSM-Paris)
DTSTART;VALUE=DATE-TIME:20211203T140000Z
DTEND;VALUE=DATE-TIME:20211203T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/44
DESCRIPTION:Title: Fractional susceptibility functions for the quadratic family.\n
by Julien Sedro (LPSM-Paris) as part of Zoominar in Dynamical Systems @ Po
rto\n\n\nAbstract\nIn the last two decades\, a clear picture of linear res
ponse for one-dimensional dynamics emerged. However\, in the specific inst
ance of the quadratic family\, two seemingly contradictory results coexist
: Ruelle proved in 2005 that the formal candidate for the derivative of th
e response function at 0 was well defined\, through the study of the susce
ptibility function\, while Baladi et al. proved in 2014 that the same resp
onse function was at best 1/2 Hölder at 0. To try to "shed some light on
this puzzling state of affairs"\, Baladi and Smania introduced so called
fractional susceptibility functions\, which are complex functions of two c
omplex variables\, and relate to fractional response in the same way the s
usceptibility function relates to linear response. I will present results
establishing holomorphy on a disk of radius larger than one for simplified
fractional susceptibility functions\, as well as explain the strategy to
extend this result to the 'true' fractional susceptibility function.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Schapira (University of Rennes)
DTSTART;VALUE=DATE-TIME:20211203T150000Z
DTEND;VALUE=DATE-TIME:20211203T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/45
DESCRIPTION:by Barbara Schapira (University of Rennes) as part of Zoominar
in Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Smania (University of São Paulo - ICMC)
DTSTART;VALUE=DATE-TIME:20211119T150000Z
DTEND;VALUE=DATE-TIME:20211119T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/46
DESCRIPTION:Title: Birkhoff sums as distributions\nby Daniel Smania (University of
São Paulo - ICMC) as part of Zoominar in Dynamical Systems @ Porto\n\n\n
Abstract\nUnder conditions (sufficiently fast decay of correlations) that
are satisfied in various settings we can consider Birkhoff sums as distrib
utions in the Schwartz sense (as in the study of PDEs) and study their reg
ularity. We will do this study in the case of piecewise expanding one-dime
nsional maps and some other cases. This study makes intensive use of the s
tatistical properties of the dynamic systems under consideration (decay of
correlations\, central limit theorem). In addition to its intrinsic inter
est\, this study is motivated by the theory of deformations of dynamical s
ystems\, something similar to Teichmuller's theory for compact Riemann sur
faces\, but in infinite dimension\, which has applications in important qu
estions about the perturbation of dynamical systems\, such as the problem
of linear response. Indeed\, in one-dimensional dynamics topological class
es often have a differentiable structure\, that is\, they are infinite-dim
ensional Banach manifolds\, and the study of Birkhoff sums as distribution
s has a surprisingly important role here. Joint work with Clodoaldo Ragazz
o (IME-USP)\, but we will also cite several results with Viviane Baladi an
d Amanda de Lima.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antti Käenmäki (University of Oulu)
DTSTART;VALUE=DATE-TIME:20211217T140000Z
DTEND;VALUE=DATE-TIME:20211217T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/47
DESCRIPTION:Title: Finer geometry of planar self-affine sets\nby Antti Käenmäki
(University of Oulu) as part of Zoominar in Dynamical Systems @ Porto\n\n\
nAbstract\nFor a planar self-affine set satisfying the strong separation c
ondition\, it has been recently proved that under mild assumptions the Hau
sdorff dimension equals the affinity dimension. In this article\, we conti
nue this line of research\, and our objective is to acquire more refined g
eometric information in this setting. In a large class of such non-carpet
planar self-affine sets\, we characterize Ahlfors regularity\, determine t
he Assouad dimension of the set and its projections\, and estimate the Hau
sdorff dimension of slices. We also demonstrate that the Assouad dimension
is not necessarily bounded above by the affinity dimension. The talk is b
ased on a recent work with Balázs Bárány and Han Yu.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Saussol (Université de Brest Occidentale)
DTSTART;VALUE=DATE-TIME:20211217T150000Z
DTEND;VALUE=DATE-TIME:20211217T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/48
DESCRIPTION:Title: Mikado of geodesics on negatively curved manifolds\nby Benoit S
aussol (Université de Brest Occidentale) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nRecently Athreya\, Lalley\, Sapir and Wrot
en have been interested in the tangle of geodesics in a compact riemaniann
surface of negative curvature. One question is to understand locally the
picture of a geodesic segment of length T\, in a vicinity of any point gi
ven on the surface. With Françoise Pène we recover their main result\, a
pplying our work on spatio-temporal point processes for visits to small se
ts.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Lizana (Universidade Federal da Bahia)
DTSTART;VALUE=DATE-TIME:20220121T140000Z
DTEND;VALUE=DATE-TIME:20220121T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/49
DESCRIPTION:Title: Invariance of entropy for maps isotopic to Anosov\nby Cristina
Lizana (Universidade Federal da Bahia) as part of Zoominar in Dynamical Sy
stems @ Porto\n\n\nAbstract\nWe prove the topological entropy remains cons
tant inside the class of partially hyperbolic diffeomorphisms of T^d with
simple central bundle (that is\, when it decomposes into one dimensional s
ub-bundles with controlled geometry) and such that their induced action on
H_1(T^d) is hyperbolic. In absence of the simplicity condition we constru
ct a robustly transitive counter-example. This is a joint work with P. Car
rasco\, E. Pujals and C. Vásquez.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Giulietti (Università di Pisa)
DTSTART;VALUE=DATE-TIME:20220204T140000Z
DTEND;VALUE=DATE-TIME:20220204T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/50
DESCRIPTION:Title: Quenched linear response for smooth expanding on average cocycles\nby Paolo Giulietti (Università di Pisa) as part of Zoominar in Dynami
cal Systems @ Porto\n\n\nAbstract\nI will present an abstract quenched li
near response result for random dynamical systems\, which applies to the c
ase of smooth expanding on average cocycles on the unit circle. Confrontin
g with the existing results in the literature\, the class of random dynam
ics studied does not necessarily exhibit uniform decay of correlations. J
oint work with D. Dragicevic (Univ. of Rijeka) and J. Sedro (Sorbonne Uni
v.)\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Andersson (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20220218T140000Z
DTEND;VALUE=DATE-TIME:20220218T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/51
DESCRIPTION:Title: Non-uniformly expanding maps in the "wrong" homotopy classes\nb
y Martin Andersson (Universidade Federal Fluminense) as part of Zoominar i
n Dynamical Systems @ Porto\n\n\nAbstract\nExamples of non-uniformly expan
ding maps are usually constructed by deforming a uniformly expanding map a
long a (locally supported) homotopy. In this talk I intend to explain how
to create new examples of non-uniformly expanding maps by deforming other
kinds of maps\, including Anosov endomorphisms.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsutoshi Shinohara (Hitotsubashi University & Université de Bou
rgogne)
DTSTART;VALUE=DATE-TIME:20220218T150000Z
DTEND;VALUE=DATE-TIME:20220218T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/52
DESCRIPTION:Title: On A/D-converters and Fredholm determinants of piecewise linear map
s\nby Katsutoshi Shinohara (Hitotsubashi University & Université de B
ourgogne) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\n
Beta-encoders are A/D (Analog-to-Digital) encoders based on beta-expansion
s. In order to give estimates of their quantization errors theoretically\,
the spectral analysis of Perron-Frobenius operators of corresponding piec
ewise linear maps\, in other words\, the study of dynamical zeta functions
\, plays an important role. I will give an introductory explanation of thi
s interplay between electronic circuit design theory and the theory of one
-dimensional dynamical systems. \nReference: Estimation of mean squared e
rrors of non-binary A/D-encoders through Fredholm determinants of piecewis
e-linear transformations https://doi.org/10.1587/nolta.9.243\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cagri Sert (University of Zurich)
DTSTART;VALUE=DATE-TIME:20220128T150000Z
DTEND;VALUE=DATE-TIME:20220128T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/53
DESCRIPTION:Title: Counting and boundary limit theorems for representations of Gromov-
hyperbolic groups\nby Cagri Sert (University of Zurich) as part of Zoo
minar in Dynamical Systems @ Porto\n\n\nAbstract\nLet $\\Gamma$ be a hyper
bolic group and S a finite symmetric generating set. The choice of S deter
mines a metric on $\\Gamma$ (namely the graph metric on the associated Cay
ley graph). Given a representation $\\rho: \\Gamma \\to \\GL_d(\\R)$\, we
are interested in obtaining results analogous to random matrix products th
eory (RMPT) but for the deterministic sequence of spherical averages (with
respect to S-metric). We will discuss a general law of large numbers and
more refined limit theorems such as central limit theorem and large deviat
ions. If time allows\, we will also see boundary limit theorems and conver
gence of interpolated matrix norms along geodesic rays to the standard Bro
wnian motion. The techniques involve the existence of a coding for hyperbo
lic groups\, RMPT in Markovian dependence and ergodicity of Patterson--Sul
livan measures. These as well as the connections with (and results in) the
classical RMPT will be discussed. Joint work with S. Cantrell.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Giordano Bruno (Università di Udine)
DTSTART;VALUE=DATE-TIME:20220204T150000Z
DTEND;VALUE=DATE-TIME:20220204T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/54
DESCRIPTION:Title: Topological and algebraic entropy on LCA groups\nby Anna Giorda
no Bruno (Università di Udine) as part of Zoominar in Dynamical Systems @
Porto\n\n\nAbstract\nSince its origin\, the algebraic entropy h_alg was i
ntroduced in connection with the topological entropy h_top by means of the
Pontryagin - van Kampen duality. For a continuous endomorphism φ: G →
G of a locally compact abelian group G\, denote by \\hat G the Pontryagin
dual group of G and by \\hat φ: G → G the dual endomorphism of φ. In t
his talk\, we see under which assumptions the equality h_top(φ) = h_alg(\
\hat φ) is known to hold. We present the same connection also in the much
more general setting of (semi)group actions.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fagner B Rodrigues (Federal University of Rio Grande do Sul)
DTSTART;VALUE=DATE-TIME:20220304T140000Z
DTEND;VALUE=DATE-TIME:20220304T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/55
DESCRIPTION:Title: Properties of the set of entropy points of a free semigroup action<
/a>\nby Fagner B Rodrigues (Federal University of Rio Grande do Sul) as pa
rt of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nThe aim of this
talk is to present some local properties of the topological entropy of a
free semigroup action. In order to do that we focus on the set of entropy
points of a free semigroup action\, show that this set carries the full en
tropy of the system (which\, with respect to the chaocity of the system\,
gives a fundamental relevance to such set). We prove that the topological
entropy of a free semigroup action focuses on a countable set of points. T
his is a joint work with Marcus V. Silva and Thomas Jacobus\, both are PhD
students of the PhD program of Mathematics and Statistics Institute of th
e Federal University of Rio Grande do Sul.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jamerson Bezerra (Copernicus University Torun)
DTSTART;VALUE=DATE-TIME:20220304T150000Z
DTEND;VALUE=DATE-TIME:20220304T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/56
DESCRIPTION:Title: Regularity of the Lyapunov exponent of random product of matrices\nby Jamerson Bezerra (Copernicus University Torun) as part of Zoominar
in Dynamical Systems @ Porto\n\n\nAbstract\nIt is well established in the
literature that the Lyapunov exponent of the random product of matrices va
ries continuously with respect to the underlying data. However\, the under
standing of the right modulus of continuity of this function remains an ac
tive problem with many contributions in the past years. In this talk we pr
esent an upper bound for the regularity of the Lyapunov exponent of random
product of (generic) matrices. This upper bound can be characterized in t
erms of metric properties of another essential invariant of the system nam
ely the stationary measure.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Baker (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20220318T140000Z
DTEND;VALUE=DATE-TIME:20220318T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/57
DESCRIPTION:Title: Normal numbers and self-similar measures\nby Simon Baker (Unive
rsity of Birmingham) as part of Zoominar in Dynamical Systems @ Porto\n\n\
nAbstract\nA real number x is said to be normal in base b if the sequence
(b^n x) is uniformly distributed modulo one. In this talk I will discuss a
recent result which states that for a self-similar measure and an integer
b\, if the self-similar measure and b satisfy a suitable arithmetic assum
ption\, then almost every x is normal in base b with respect to the self-s
imilar measure. This is a joint work with Amir Algom and Pablo Shmerkin.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danijela Damjanovic (KTH)
DTSTART;VALUE=DATE-TIME:20220318T150000Z
DTEND;VALUE=DATE-TIME:20220318T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/58
DESCRIPTION:Title: Exploring the Borel-Smale example: centralizer rigidity for maps an
d center rigidity for the action\nby Danijela Damjanovic (KTH) as part
of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nI will talk about
our exploration of an interesting Z^2 Anosov action on a 2-step nilmanifo
ld. Historically\, Anosov elements of this action were presented by Smale
as first examples of Anosov maps which are not on the torus. We provide c
lassification of centralizers for perturbations of certain non-Anosov elem
ents of this action. We also show that the action itself is not locally ri
gid\, but it still enjoys certain center-rigidity property under perturbat
ions. This is joint work with Amie Wilkinson and Disheng Xu.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoo Yokoyama (Gifu University)
DTSTART;VALUE=DATE-TIME:20220408T130000Z
DTEND;VALUE=DATE-TIME:20220408T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/59
DESCRIPTION:Title: Existence and Non-existence of Length Averages for Foliations\n
by Tomoo Yokoyama (Gifu University) as part of Zoominar in Dynamical Syste
ms @ Porto\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Spiewak (Bar-Ilan University)
DTSTART;VALUE=DATE-TIME:20220422T130000Z
DTEND;VALUE=DATE-TIME:20220422T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/60
DESCRIPTION:Title: Typical absolute continuity for classes of dynamically defined meas
ures\nby Adam Spiewak (Bar-Ilan University) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nConsider a one-parameter family of i
terated function systems on the interval and a family of measures on the c
orresponding symbolic space\, depending on the same parameter. We study ge
ometric properties of measures projected by the natural projection corresp
onding to the IFS. Assuming that IFS satisfies a transversality condition
and measures depend on the parameter regularly enough\, we obtain results
on the value of the dimension and absolute continuity of the projected me
asure for almost every parameter. This extends classical results (for proj
ections of a fixed measure) and applies e.g. to invariant measures for sys
tems with place-dependent probabilities and equilibrium measures for hyper
bolic iterated function systems. The talk is based on a recent joint work
with Balázs Bárány\, Károly Simon and Boris Solomyak.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastien Alvarez (Universidad de la Republica)
DTSTART;VALUE=DATE-TIME:20220408T140000Z
DTEND;VALUE=DATE-TIME:20220408T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/61
DESCRIPTION:Title: Metric entropy of foliations\nby Sebastien Alvarez (Universidad
de la Republica) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAb
stract\nThe topological dynamiucs of foliations is wll understood. There i
s an analogue of periodic orbits\, limit sets\, recurrence\, and even topo
logical entropy\, following the work of Ghys\, Langevin and Walczak. This
entropy measures the transverse separation of the leaves of a foliation. T
his is not the case of the ergodic theory of foliations. In particular\, t
here is no satisfactory version of metric entropy for foliations\, and it
is difficult to imagine a way to detect the separation of leaves using mea
sure theory (whether harmonic\, or invariant by certain dynamics tangent t
o the leaves). For example is it possible to obtain a variational principl
e for foliations? In this talk\, I will discuss an approach made with Jiag
ang Yang (UFF\, Niteroi) to attack this problem.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Zelerowicz (University of Maryland)
DTSTART;VALUE=DATE-TIME:20220422T140000Z
DTEND;VALUE=DATE-TIME:20220422T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/62
DESCRIPTION:Title: Lorentz gases on aperiodic tilings\nby Agnieszka Zelerowicz (Un
iversity of Maryland) as part of Zoominar in Dynamical Systems @ Porto\n\n
\nAbstract\nIn this joint work with Rodrigo Treviño we consider the Lore
ntz gas model of category A (that is\, with no corners and of finite horiz
on) on aperiodic repetitive tilings of $\\mathbb{R}^2$ of finite local com
plexity. We show that the compact factor of the collision map has the K pr
operty\, from which we derive mixing for pattern-equivariant functions as
well as the planar ergodicity of the Lorentz gas flow.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Disheng Xu (Beijing University)
DTSTART;VALUE=DATE-TIME:20220506T130000Z
DTEND;VALUE=DATE-TIME:20220506T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/63
DESCRIPTION:Title: Some topics on compact center foliations of partially hyperbolic sy
stems\nby Disheng Xu (Beijing University) as part of Zoominar in Dynam
ical Systems @ Porto\n\n\nAbstract\nPartially hyperbolic systems is a natu
ral generalization of Anosov systems in dynamical systems. In this talk we
will focus on partially hyperbolic systems with invariant compact center
foliations\, and discuss some interesting properties and some recent resul
ts on the regularity of compact center foliations\, under different condit
ions. This talk will be self-contained.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma D'Aniello (Universitá di Campania)
DTSTART;VALUE=DATE-TIME:20220603T140000Z
DTEND;VALUE=DATE-TIME:20220603T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/64
DESCRIPTION:Title: Some linear dynamics on Lp spaces\nby Emma D'Aniello (Universit
á di Campania) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbst
ract\nWe investigate\, in the linear setting\, notions of chaos coming fro
m topological dynamics\, and hyperbolic properties originally defined in a
non-linear framework. We focus in particular on “shift-like” composi
tion operators on arbitrary measure spaces\, a large class of linear opera
tors that includes the weighted shifts as a special case.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luciana Salgado (Universidade Federal do Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20220506T140000Z
DTEND;VALUE=DATE-TIME:20220506T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/65
DESCRIPTION:Title: Ergodic and geometric aspects of singular flows\nby Luciana Sa
lgado (Universidade Federal do Rio de Janeiro) as part of Zoominar in Dyna
mical Systems @ Porto\n\n\nAbstract\nLyapunov functions provided by quadra
tic forms are useful tools in Dynamical Systems. For instance\, these are
used in results of topological stability and ergodic properties as found
in works by Burns-Katok\, Lewowicz\, Markarian and Wojtkowski. This talk
is about how to use the quadratic Lyapunov functions to show some ergodic
and dynamical properties of singular flows (e.g. Lorenz flow).\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Héctor Barge (Universidad Politécnica de Madrid)
DTSTART;VALUE=DATE-TIME:20220520T140000Z
DTEND;VALUE=DATE-TIME:20220520T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/66
DESCRIPTION:Title: Low-dimensional topology and the realization problem of attractors
for non-connected compacta\nby Héctor Barge (Universidad Politécnica
de Madrid) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract
\nIt is well known that if K = K_1 ⊔ . . . ⊔ K_r ⊂ R^n\, where K_i i
s compact for each i\, is an attractor for a dynamical system (discrete or
continuous) in R^n then K_i is an attractor for each i. In this talk we s
hall study whether the converse statement holds:\n\n(S): If each K_i is an
attractor for a dynamical system so is K.\n\nWe shall see that (S) holds
true in the case of continuous dynamical systems. However\, the discrete c
ase is more involved. In particular\, we will see that there exist compact
a in R^3 comprised of two connected components that can be realized as att
ractors separately but whose union cannot be so realized. Finally\, we wil
l introduce a sufficient condition for (S) to hold true in the discrete ca
se and we shall see that this condition is also sufficient in some suitabl
e situations. These results have been obtained in collaboration with J.J.
Sanchez-Gabites.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adriana Sanchez (CIMPA - Costa Rica)
DTSTART;VALUE=DATE-TIME:20220603T130000Z
DTEND;VALUE=DATE-TIME:20220603T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/67
DESCRIPTION:Title: Analiticity of the Lyapunov exponents of random products of quasi-p
eriodic cocycles\nby Adriana Sanchez (CIMPA - Costa Rica) as part of Z
oominar in Dynamical Systems @ Porto\n\n\nAbstract\nOne of the most import
ant questions that comes up when studying Lyapunov exponents of linear coc
ycles is the regularity problem. By this we mean the problem of understand
ing the behavior of the Lyapunov exponents regarding the underlying data.
It is a classical result of Peres [1] that\, for i.i.d. sequence of matric
es with discrete distribution\, the Lyapunov exponents are locally analyti
c if mild simplicity conditions are assumed. In this talk we are going to
discuss an extension of Per ́es conclusions in [1] to include the random
product of quasi-periodic cocycles for the skew product base dynamics. Thi
s is a join work with Jamerson Bezerra and El Hadji Yaya Tall.\n\n[1] Y. P
eres. “Analytic dependence of Lyapunov exponents on transition probabil-
ities”. In: Lyapunov exponents (Oberwolfach\, 1990). Vol. 1486. Lecture
Notes in Math. Springer-Verlag\, 1991\, pp. 64–80.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Cerreia-Vioglio (Bocconi)
DTSTART;VALUE=DATE-TIME:20220520T130000Z
DTEND;VALUE=DATE-TIME:20220520T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/68
DESCRIPTION:Title: Ergodic Theorems for Lower Probabilities\nby Simone Cerreia-Vio
glio (Bocconi) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstr
act\nWe establish an Ergodic Theorem for lower probabilities\, a generaliz
ation of standard probabilities widely used in applications. As a by-produ
ct\, we provide a version for lower probabilities of the Strong Law of Lar
ge Numbers (joint work with F. Maccheroni and M. Marinacci).\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Freitas (University of Porto)
DTSTART;VALUE=DATE-TIME:20220617T130000Z
DTEND;VALUE=DATE-TIME:20220617T135000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/69
DESCRIPTION:Title: Point processes\, record events and heavy tails\nby Jorge Freit
as (University of Porto) as part of Zoominar in Dynamical Systems @ Porto\
n\n\nAbstract\nWe consider stochastic processes arising from chaotic syste
ms and build multidimensional point processes which provide a nice descrip
tion regarding both the extremal behaviour\, the distribution of record ev
ents and the convergence of functional limits for the sums of heavy tailed
observables.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minsung Kim (Copernicus University in Torún)
DTSTART;VALUE=DATE-TIME:20220617T135000Z
DTEND;VALUE=DATE-TIME:20220617T144000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/70
DESCRIPTION:Title: Deviation spectrum of Birkhoff integrals for locally Hamiltonian f
lows on compact surfaces\nby Minsung Kim (Copernicus University in Tor
ún) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nThis
talk will consist of an introduction to the topic of deviation of Birkhoff
integrals for locally Hamiltonian flows on compact surfaces and recent re
lated results. These works extend the study of the spectrum of deviations
of ergodic integrals beyond the case where the observable vanishes at the
singularities. New developments include a better understanding of the asym
ptotics (in non-degenerate regime) and the appearance of new exponents in
the deviation spectrum (in degenerate regime). This is joint work with Krz
ysztof Frączek.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanja Schindler (University of Vienna)
DTSTART;VALUE=DATE-TIME:20220617T145000Z
DTEND;VALUE=DATE-TIME:20220617T154000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/71
DESCRIPTION:Title: A qualitative central limit theorem for certain unbounded over piec
ewise expanding interval map\nby Tanja Schindler (University of Vienna
) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nMany lim
it theorems in ergodic theory are proven using the spectral gap method. So
one of the main ingredients for this method is to have a space on which t
he transfer operator has a spectral gap. However\, most of the classical s
paces\, like for example the space of Hölder or quasi-Hölder function or
BV functions don't allow unbounded functions. We will give such a space w
hich allows observables with a pole at the fixed points of a piecewise exp
anding interval transformation and state a quantitative central limit theo
rem using Edgeworth expansions. As an application we give a sampling resul
t for the Riemann-zeta function over a Boolean type transformation. This i
s joint work with Kasun Fernando.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sakshi Jain (Università degli Studi di Roma - Tor Vergata)
DTSTART;VALUE=DATE-TIME:20220916T130000Z
DTEND;VALUE=DATE-TIME:20220916T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/72
DESCRIPTION:Title: Discontinuities cause essential spectrum\nby Sakshi Jain (Unive
rsità degli Studi di Roma - Tor Vergata) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe study transfer operators associated to
piecewise monotone interval transformations and show that the essential sp
ectrum is large for any relevant Banach space when the transformation fail
s to be Markov. Constructing a family of Banach spaces we show that the lo
wer bound on the essential spectral radius is optimal. Indeed\, these Bana
ch spaces realise an essential spectral radius as close as desired to the
theoretical best possible case.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlene Kalle (University of Leiden)
DTSTART;VALUE=DATE-TIME:20220930T130000Z
DTEND;VALUE=DATE-TIME:20220930T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/73
DESCRIPTION:Title: Random intermittent dynamics\nby Charlene Kalle (University of
Leiden) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nIn
termittent dynamics\, where systems irregularly alternate between long per
iods of different types of dynamical behaviour\, has been studied since th
e work of Pomeau and Manneville in 1980. In random dynamical systems this
phenomenon has only been well understood in a few specific cases. A random
dynamical system consists of a family of deterministic systems\, one of w
hich is chosen to be applied at each time step according to some probabili
stic rule. In this talk we will describe the intermittency of some familie
s of random systems with a particular emphasis on how the intermittency of
the random system depends on the intermittency of the underlying determin
istic systems. This talk is based on joint works with Ale Jan Homburg\, To
m Kempton\, Valentin Matache\, Marks Ruziboev\, Masato Tsujii\, Evgeny Ver
bitskiy and Benthen Zeegers.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Moreira (University of Warwick)
DTSTART;VALUE=DATE-TIME:20221014T130000Z
DTEND;VALUE=DATE-TIME:20221014T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/74
DESCRIPTION:Title: Infinite Ergodic Ramsey theory\nby Joel Moreira (University of
Warwick) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nI
n the 1970's Furstenberg obtained an ergodic theoretic proof of Szemeredi'
s theorem\, stating that any set of natural numbers with positive upper de
nsity contains arbitrarily long (but finite) arithmetic progressions. Sinc
e then\, Furstenbeg's approach has been extended to many other combinatori
al applications\, giving rise to the field of Ergodic Ramsey Theory. Howev
er\, until recently\, ergodic theoretic methods were unable to handle infi
nite configurations. I will present recent joint work where we overcame th
is difficulty to answer some Ramsey theoretical questions raised by Erdos
in the 1980's using methods from ergodic theory.\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ai-Hua Fan (Université de Picardie Jules Verne\, Amiens)
DTSTART;VALUE=DATE-TIME:20221028T130000Z
DTEND;VALUE=DATE-TIME:20221028T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T052541Z
UID:Zoominar-CMUP/75
DESCRIPTION:by Ai-Hua Fan (Université de Picardie Jules Verne\, Amiens) a
s part of Zoominar in Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Zoominar-CMUP/75/
END:VEVENT
END:VCALENDAR
~~