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BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto (Canada))
DTSTART;VALUE=DATE-TIME:20200514T150000Z
DTEND;VALUE=DATE-TIME:20200514T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/1
DESCRIPTION:Title: Central limit theorems for counting measures in coarse negative curvature
\nby Giulio Tiozzo (University of Toronto (Canada)) as part of DinAmic
I: Another Internet Seminar\n\n\nAbstract\nWe establish general central li
mit theorems for an action of a group on a hyperbolic space with respect t
o counting for the word length in the group.\nIn 2013\, Chas\, Li\, and Ma
skit produced numerical experiments on random closed geodesics on a hyperb
olic pair of pants. Namely\, they drew uniformly at random conjugacy clas
ses of a given word length\, and considered the hyperbolic length of the
corresponding closed geodesic on the pair of pants. Their experiments l
ead to the conjecture that the length of these closed geodesics satisfies
a central limit theorem\, and we proved this conjecture in 2018. \nIn our
new work\, we remove the assumptions of properness and smoothness of the
space\, or cocompactness of the action\, thus proving a general central li
mit theorem for group actions on hyperbolic spaces. \nWe will see how our
techniques replace the classical thermodynamic formalism and allow us to
provide new applications\, including to lengths of geodesics in geometrica
lly finite manifolds and to intersection numbers with submanifolds.\nJoint
work with I. Gekhtman and S. Taylor.\n\nZoom link:\nhttps://unipd.zoom.us
/j/91001776009?pwd=Qm0wZVF3TWxmNm9LVFhYL0RiczBHdz09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Leguil (Université Paris-Sud 11 (France))
DTSTART;VALUE=DATE-TIME:20200521T150000Z
DTEND;VALUE=DATE-TIME:20200521T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/2
DESCRIPTION:Title: Some rigidity results for billiards and hyperbolic flows\nby Martin L
eguil (Université Paris-Sud 11 (France)) as part of DinAmicI: Another Int
ernet Seminar\n\n\nAbstract\nIn a project with P. Bálint\, J. De Simoi an
d V. Kaloshin\, we have been studying the inverse problem for a class of o
pen dispersing billiards obtained by removing from the plane a finite numb
er of smooth strictly convex scatterers satisfying a non-eclipse condition
. The dynamics of such billiards is hyperbolic (Axiom A)\, and there is a
natural labeling of periodic orbits. We show that it is generically possib
le\, in the analytic category and for billiard tables with two (partial) a
xial symmetries\, to determine completely the geometry of those billiards
from the purely dynamical data encoded in their Marked Length Spectrum (le
ngths of periodic orbits + marking). An important step is the obtention of
asymptotic estimates for the Lyapunov exponents of certain periodic point
s accumulating a reference periodic point\, which turn out to be useful in
the study of other rigidity problems. In particular\, I will explain the
results obtained in a joint work with J. De Simoi\, K. Vinhage and Y. Yang
on the question of entropy rigidity for 3-dimensional Anosov flows and di
spersing billiards.\n\nZoom link: https://unipd.zoom.us/j/98220838792?pwd=
Njg2U1pnQXQ3Uno4Nit0RE13MzFnQT09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Cellarosi (Queen’s University (Canada))
DTSTART;VALUE=DATE-TIME:20200528T150000Z
DTEND;VALUE=DATE-TIME:20200528T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/3
DESCRIPTION:Title: Rational Horocycle lifts and the tails of Quadratic Weyl sums\nby Fra
ncesco Cellarosi (Queen’s University (Canada)) as part of DinAmicI: Anot
her Internet Seminar\n\n\nAbstract\nEquidistribution of horocycles on hype
rbolic surfaces has been used to dynamically answer several probabilistic
questions about number-theoretical objects. In this talk we focus on horoc
ycle lifts\, i.e. curves on higher-dimensional manifolds whose projection
to the hyperbolic surface is a classical horocycle\, and their behaviour u
nder the action of the geodesic flow. It is known that when such horocycle
lifts are `generic’\, then their push forward via the geodesic flow bec
omes equidistributed in the ambient manifold. We consider certain ‘non-g
eneric’ (i.e. rational) horocycle lifts\, in which case the equidistribu
tion takes place on a sub-manifold. We then use this fact to study the tai
l distribution of quadratic Weyl sums when one of their arguments is rando
m and the other is rational. In this case we obtain random variables with
heavy tails\, all of which only possess moments of order less than 4. Depe
nding on the rational argument\, we establish the exact tail decay\, which
can be described with the help of the Dedekind $\\psi$-function.\n\nJoint
work with Tariq Osman.\n\nZoom link: https://unipd.zoom.us/j/91625758001?
pwd=NzU1SG5LZkxKVTI5SXBsSUpNUW5XQT09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Vaienti (Centre de Physique Théorique\, Marseille (France)
)
DTSTART;VALUE=DATE-TIME:20200604T150000Z
DTEND;VALUE=DATE-TIME:20200604T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/4
DESCRIPTION:Title: Thermodynamic formalism for random weighted covering systems\nby Sand
ro Vaienti (Centre de Physique Théorique\, Marseille (France)) as part of
DinAmicI: Another Internet Seminar\n\n\nAbstract\nWe develop a quenched t
hermodynamic formalism for random dynamical systems generated by countably
branched\, piecewise-monotone mappings of the interval that satisfy a ran
dom covering condition.\n\nJoint with J. Atnip\, G. Froyland and C. Gonzal
ez-Tokman\n\nZoom link: https://unipd.zoom.us/j/91644787447?pwd=UzZIbXg4Qm
s3NU9lek5Hd1dLZGR1Zz09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Maggioni (Leiden University)
DTSTART;VALUE=DATE-TIME:20200701T150000Z
DTEND;VALUE=DATE-TIME:20200701T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/5
DESCRIPTION:Title: Matching for random systems with an application to minimal weight expansi
ons\nby Marta Maggioni (Leiden University) as part of DinAmicI: Anothe
r Internet Seminar\n\n\nAbstract\nWe consider families of skew-product map
s\, representing systems evolving in discrete time in which\, at each time
step\, one of a number of transformations is chosen according to an i.i.d
process and applied. We extend the notion of matching for such dynamical
systems and we show that\, for a certain family of piecewise affine random
maps of the interval\, the property of random matching implies that any i
nvariant density is piecewise constant. We give an application by introduc
ing a one-parameter family of random maps generating signed binary expansi
ons of numbers. This family has random matching for Lebesgue almost every
parameter\, producing matching intervals that are related to the ones obta
ined for the Nakada continued fraction transformations. We use this proper
ty to study the expansions with minimal weight.\nJoint with K. Dajani\, an
d C. Kalle\n\nZoom link: https://unipd.zoom.us/j/98457166023?pwd=Q1VSZUtEb
k95QnVUYmVGVEpQMXk5UT09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunrose Shrestha (Tufts University\, USA)
DTSTART;VALUE=DATE-TIME:20200617T150000Z
DTEND;VALUE=DATE-TIME:20200617T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/7
DESCRIPTION:Title: The topology and geometry of random square-tiled surfaces\nby Sunrose
Shrestha (Tufts University\, USA) as part of DinAmicI: Another Internet S
eminar\n\n\nAbstract\nA square-tiled surface (STS) is a branched cover of
the standard square torus with branching over exactly one point. They are
concrete examples of translation surfaces which are an important class of
singular flat metrics on 2-manifolds with applications in Teichmüller the
ory and polygonal billiards. In this talk we will consider a randomizing m
odel for STSs based on permutation pairs and use it to compute the genus d
istribution. We also study holonomy vectors (Euclidean displacement vector
s between cone points) on a random STS. Holonomy vectors of translation su
rfaces provide coordinates on the space of translation surfaces and their
enumeration up to a fixed length has been studied by various authors such
as Eskin and Masur. In this talk\, we obtain finer information about the s
et of holonomy vectors\, Hol(S)\, of a random STS. In particular\, we will
see how often Hol(S) contains the set of primitive integer vectors and fi
nd how often these sets are exactly equal.\n\nZoom link: https://unipd.zoo
m.us/j/92074073847?pwd=ZDd6Y28yUVowcjJNUFFRYU52WGtTdz09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Knauf (Friedrich-Alexander-Universität Erlangen-Nürnberg
)
DTSTART;VALUE=DATE-TIME:20200624T150000Z
DTEND;VALUE=DATE-TIME:20200624T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/8
DESCRIPTION:Title: Asymptotic velocity for scattering particles\nby Andreas Knauf (Fried
rich-Alexander-Universität Erlangen-Nürnberg) as part of DinAmicI: Anoth
er Internet Seminar\n\n\nAbstract\nPartly with Jacques Fejoz\, Richard Mon
tgomery\, Stefan Fleischer and Manuel Quaschner.\n\nThe past and future of
scattering particle systems is partly determined by their asymptotic velo
city\, that is\, the Cesàro limit of the velocity. That this exists for b
ounded interactions and all initial conditions\, is part of a statement so
metimes called ‘asymptotic completeness’. The same statement does not
apply to individual initial conditions in celestial mechanics. However\, a
t least for up to four particles\, nonexistence of asymptotic velocity is
a measure zero phenomenon. We explain some new ideas connected with the pr
oof (Poincaré section techniques for wandering sets\, non-deterministic p
article systems\, and walks on a poset of set partitions).\n\nZoom link: h
ttps://unipd.zoom.us/j/96933860238?pwd=c1pEamVCOVJNci9MVThZWWlzeGt6UT09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Françoise Pène (Université de Bretagne Occidentale (France))
DTSTART;VALUE=DATE-TIME:20200708T150000Z
DTEND;VALUE=DATE-TIME:20200708T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/9
DESCRIPTION:Title: Invariance by induction of the asymptotic variance\nby Françoise Pè
ne (Université de Bretagne Occidentale (France)) as part of DinAmicI: Ano
ther Internet Seminar\n\n\nAbstract\nIt is well known that the integral of
an observable is preserved by induction. We are interested here in extens
ions of this result to moments of order 2 and 3. We have two natural candi
dates for the second and third order moments: the classical asymptotic var
iance (given by the Green-Kubo formula) and an analogous quantity of the t
hird order. This question arises from the proof of CLT. In some cases\, th
e asymptotic variance in the CLT can be expressed on the one hand in terms
of the classical Green-Kubo formula and on the other hand in terms of the
Green-Kubo formula for the induced system. Under general assumptions (inv
olving transfer operators)\, we prove that the asymptotic variance is pres
erved by induction and that the natural third order quantity is preserved
up to an error term.\n\nThis is joint work with Damien Thomine.\n\nzoom li
nk: https://unipd.zoom.us/j/95330010741?pwd=ZXBpejY0ZUNiQUVkdXFrcnF0RW81UT
09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Marò (University of Pisa (Italy))
DTSTART;VALUE=DATE-TIME:20201112T150000Z
DTEND;VALUE=DATE-TIME:20201112T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/10
DESCRIPTION:Title: Chaotic motion in the breathing circle billiard\nby Stefano Marò (U
niversity of Pisa (Italy)) as part of DinAmicI: Another Internet Seminar\n
\n\nAbstract\nWe consider the free motion of a point particle inside a cir
cular billiard with periodically moving boundary\, with the assumption tha
t the collisions of the particle with the boundary are elastic so that the
energy of the particle is not preserved. It is known that if the motion o
f the boundary is regular enough then the energy is bounded due to the exi
stence of invariant curves. We show that it is nevertheless possible that
the motion of the particle is chaotic\, also under regularity assumptions
for the moving boundary. More precisely\, we show that there exists a clas
s of functions describing the motion of the boundary for which the billiar
d map admits invariant probability measures with positive metric entropy.
The proof relies on variational techniques based on Aubry-Mather theory. \
nJoint work with Claudio Bonanno.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaia Nisoli (Universidade Federal do Rio de Janeiro (Brazil))
DTSTART;VALUE=DATE-TIME:20201116T130000Z
DTEND;VALUE=DATE-TIME:20201116T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/11
DESCRIPTION:Title: A simple system presenting Noise Induced Order\nby Isaia Nisoli (Uni
versidade Federal do Rio de Janeiro (Brazil)) as part of DinAmicI: Another
Internet Seminar\n\n\nAbstract\nIn this talk I will present a family of o
ne dimensional systems with random additive noise such that\, as the noise
size increases\, the Lyapunov exponent of the stationary measure transiti
ons from positive to negative. This phenomena is known in literature as No
ise Induced Order\, and was first observed in a model of the Belosouv-Zhab
otinsky reaction and its existence was proven only recently by Galatolo-Mo
nge-Nisoli. In the talk I will show how this phenomena is strictly connect
ed with non-uniform hyperbolicity and the coexistence of regions of expans
ion and contraction in phase space\; the result is attained through a resu
lt on the continuity of the Lyapunov exponent of the stationary measure wi
th respect to the size of the noise.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (University of Rome Tor Vergata (Italy))
DTSTART;VALUE=DATE-TIME:20201210T150000Z
DTEND;VALUE=DATE-TIME:20201210T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/12
DESCRIPTION:Title: Locating Ruelle-Pollicott resonances\nby Carlangelo Liverani (Univer
sity of Rome Tor Vergata (Italy)) as part of DinAmicI: Another Internet Se
minar\n\n\nAbstract\nWe study the spectrum of transfer operators associate
d to various dynamical systems. Our aim is to obtain precise information o
n discrete spectrum. To this end we propose a unitary approach. We conside
r various settings where new information can be obtained following differe
nt branches along the proposed path. These settings include affine expandi
ng Markov maps\, uniformly expanding Markov maps\, non-uniformly expanding
maps\, hyperbolic diffeomorphisms. We believe this to be the germ of a ge
neral theory. Joint work with O. Butterley and N. Kiamari.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Miriam Benini (University of Parma (Italy))
DTSTART;VALUE=DATE-TIME:20201126T160000Z
DTEND;VALUE=DATE-TIME:20201126T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/13
DESCRIPTION:Title: Infinite entropy for transcendental entire functions\nby Anna Miriam
Benini (University of Parma (Italy)) as part of DinAmicI: Another Interne
t Seminar\n\n\nAbstract\nDefining entropy on noncompact metric spaces is a
tricky business\, since there are several natural and nonequivalent gener
alizations of the usual notions of entropy for continuous maps on compact
spaces. By defining entropy for transcendental maps on the complex plane a
s the sup over the entropy restricted to compact forward invariant subsets
\, we prove that with this definition the entropy of such functions is inf
inite. The proof relies on covering results which are distinctive to holom
orphic maps.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Venturelli (Université d'Avignon (France))
DTSTART;VALUE=DATE-TIME:20210114T150000Z
DTEND;VALUE=DATE-TIME:20210114T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/14
DESCRIPTION:Title: Hyperbolic motion in the Newtonian N-body problem with arbitrary limit s
hape\nby Andrea Venturelli (Université d'Avignon (France)) as part of
DinAmicI: Another Internet Seminar\n\n\nAbstract\nWe prove for the N-body
problem the existence of hyperbolic motions for any prescribed limit shap
e and any given initial configuration of the bodies. The energy level h>0
of the motion can also be chosen arbitrarily. Our approach is based on the
construction of a global viscosity solutions for the Hamilton-Jacobi equa
tion H(x\,du(x))=h. Our hyperbolic motion is in fact a calibrating curve o
f the viscosity solution. The presented results can also be viewed as a ne
w application of Marchal’s theorem\, whose main use in recent literature
has been to prove the existence of periodic orbits. Joint work with Ezequ
iel Maderna.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Gianfelice (Università della Calabria (Italy))
DTSTART;VALUE=DATE-TIME:20210128T150000Z
DTEND;VALUE=DATE-TIME:20210128T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/15
DESCRIPTION:Title: Stochastic stability of classical Lorenz flow under impulsive type forci
ng\nby Michele Gianfelice (Università della Calabria (Italy)) as part
of DinAmicI: Another Internet Seminar\n\n\nAbstract\nInspired by the prob
lem of modeling the so called anthropogenic forcing in climatology\, e.g.
the effects of the emissions of greenhouse gases in the atmosphere\, we in
troduce a novel type of random perturbation for the classical Lorenz flow
and prove its stochastic stability. The perturbation acts on the system in
an impulsive way\, hence is not of diffusive type. Namely\, given a cross
-section M for the unperturbed flow\, each time the trajectory of the syst
em crosses M the phase velocity field is changed with a new one sampled at
random from a suitable neighborhood of the unperturbed one. The resulting
random evolution is therefore described by a piecewise deterministic Mark
ov process. The proof of the stochastic stability for the unperturbed flow
is then carried on working either in the framework of the Random Dynamica
l Systems or in that of semi-Markov processes. Joint work with Sandro Vaie
nti.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Froyland (University of New South Wale)
DTSTART;VALUE=DATE-TIME:20210204T090000Z
DTEND;VALUE=DATE-TIME:20210204T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/16
DESCRIPTION:Title: The dynamic ocean\nby Gary Froyland (University of New South Wale) a
s part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nThe circulatio
n of our oceans strongly influences climate\, weather and biology. Our oce
an currents are dynamic\, and fluctuate to varying extents. I will introdu
ce data-driven numerical tools that can tease apart dynamic components of
the ocean\, with information sourced from ocean drifters\, satellite image
ry\, and ocean models. These components\, their lifecycles\, and their res
ponse to external forcing\, help us to build a dynamic picture of our ocea
n.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Bialy (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210211T150000Z
DTEND;VALUE=DATE-TIME:20210211T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/17
DESCRIPTION:Title: Birkhoff-Poritsky conjecture for centrally-symmetric billiards\nby M
isha Bialy (Tel Aviv University) as part of DinAmicI: Another Internet Sem
inar\n\n\nAbstract\nIn this talk I shall discuss Birkhoff-Poritsky conject
ure for centrally-symmetric $C^2$-smooth convex planar billiards. \n\nWe a
ssume that the domain $\\mathcal A$ between the invariant curve of $4$-per
iodic orbits and the boundary of the phase cylinder is foliated by $C^0$-i
nvariant curves. \nUnder this assumption we prove that the billiard curve
is an ellipse.\nOther versions of Birkhoff-Poritsky conjecture follow fro
m this result. \nFor the original Birkhoff-Poritsky formulation we show th
at if a neighborhood of the boundary of billiard domain has\na $C^1$-smoot
h foliation by convex caustics of rotation numbers in the interval (0\; 1/
4]\nthen the boundary curve is an ellipse. \n\nThe main ingredients of the
proof are:\n\n \n(1) the non-standard generating function for convex bill
iards\; \n\n(2) the remarkable structure of the invariant curve consistin
g of $4$-periodic orbits\; and\n\n \n(3) the integral-geometry approach in
itiated in\n\\cite{B0}\, \\cite{B1} for rigidity results of circular billi
ards. \n\n\nSurprisingly\, we establish a Hopf-type rigidity for billiards
in the ellipse.\nBased on a joint work with Andrey E. Mironov (Novosibirs
k).\n
LOCATION:https://researchseminars.org/talk/DinAmicI/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Giulietti (Università di Pisa)
DTSTART;VALUE=DATE-TIME:20210225T150000Z
DTEND;VALUE=DATE-TIME:20210225T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/18
DESCRIPTION:Title: Infinite mixing for accessible skew products\nby Paolo Giulietti (Un
iversità di Pisa) as part of DinAmicI: Another Internet Seminar\n\n\nAbst
ract\nI will present some decay of correlations results on skew products w
hich are locally accessible. The results rely on the study of a twisted tr
ansfer operator and could be generalized to many other situations. I will
also present numerical counterparts to such results.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro del Pino Gómez (Utrecht University (The Netherlands))
DTSTART;VALUE=DATE-TIME:20210325T150000Z
DTEND;VALUE=DATE-TIME:20210325T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/19
DESCRIPTION:Title: Billiards in subriemannian geometry\nby Álvaro del Pino Gómez (Utr
echt University (The Netherlands)) as part of DinAmicI: Another Internet S
eminar\n\n\nAbstract\nWhen one considers manifolds with boundary\, billiar
d dynamics are the natural analogue of standard geodesic dynamics. Namely\
, instead of having geodesics escape at the boundary\, we force them back
into the manifold using the reflection law. In other dynamical settings\,
similar constructions are possible: In 2006\, B. Khesin and S. Tabachnikov
initiated the study of billiards in the semiriemannian setting\, studying
the integrability of various tables. In recent years we have also seen th
e appearance of several billiard setups of symplectic nature.\n\nIn this t
alk I will discuss recent work with L. Dahinden in which we look at billia
rds in subriemannian geometry. I will sketch how the reflection law arises
naturally both from the control-theoretical and symplectic perspectives\,
how the reflection is problematic at tangency points between the distribu
tion and the boundary of the table\, and I will introduce some concrete ex
amples. My ultimate goal will be to pose several intriguing open questions
.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda & Daniel Peralta-Salas (UPC Barcelona & ICMAT Madrid (
Spain))
DTSTART;VALUE=DATE-TIME:20210408T140000Z
DTEND;VALUE=DATE-TIME:20210408T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/20
DESCRIPTION:Title: Looking at Euler flows through a contact mirror: Universality and Turing
completeness\nby Eva Miranda & Daniel Peralta-Salas (UPC Barcelona &
ICMAT Madrid (Spain)) as part of DinAmicI: Another Internet Seminar\n\n\nA
bstract\nThe dynamics of an inviscid and incompressible fluid flow on a Ri
emannian manifold is governed by the Euler equations. Recently\, Tao launc
hed a programme to address the global existence problem for the Euler and
Navier Stokes equations based on the concept of universality. Inspired by
this proposal\, we show that the stationary Euler equations exhibit severa
l universality features\, In the sense that\, any non-autonomous flow on a
compact manifold can be extended to a smooth stationary solution of the E
uler equations on some Riemannian manifold of possibly higher dimension. \
nThese results can be viewed as lending support to the intuition that solu
tions to the Euler equations can be extremely complicated in nature.\nA ke
y point in the proof is looking at the h-principle in contact geometry thr
ough a contact mirror\, unveiled by Sullivan\, Etnyre and Ghrist more than
two decades ago.\n\nWe end up this talk addressing an apparently differen
t question: What kind of physics might be non-computational? Using the for
mer universality result\, we can establish the Turing completeness of the
steady Euler flows\, i.e.\, there exist solutions that encode a universal
Turing machine and\, in particular\, these solutions have undecidable tra
jectories.. But\, in view of the increase of dimension yielded by our proo
f. The question is can this be done in dimension 3? We will prove the exis
tence of Turing complete fluid\nflows on a 3-dimensional geometric domain.
Our novel strategy uses the computational power of symbolic dynamics and
the contact mirror again.\n\nThis talk is based on joint work with Robert
Cardona and Fran Presas ( arXiv:1911.01963 and arXiv:2012.12828 )\n
LOCATION:https://researchseminars.org/talk/DinAmicI/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Della Corte (Università di Camerino (Italy))
DTSTART;VALUE=DATE-TIME:20210311T160000Z
DTEND;VALUE=DATE-TIME:20210311T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/21
DESCRIPTION:Title: The simplest erasing substitution\nby Alessandro Della Corte (Univer
sità di Camerino (Italy)) as part of DinAmicI: Another Internet Seminar\n
\n\nAbstract\nThe symbolic action of a substitution on the binary expansio
n generates naturally an interval map. In case of erasing substitutions\,
the map is typically Baire-1 and not Darboux. As a model case\, we conside
r what is arguably the simplest erasing substitution\, mapping 0s to the e
mpty word and 1s to 0 or 1 depending on the parity. The corresponding inte
rval map is shown to have fractal properties (bounds are given on the Haus
dorff dimension of the fibers) and to display rich dynamical behavior\, in
cluding Devaney chaos\, uniform distributional chaos of type 1\, infinite
topological entropy as well as the presence of cycles attracting in a fini
te time every rational.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanja Schindler (Scuola Normale Superiore di Pisa (Italy))
DTSTART;VALUE=DATE-TIME:20210422T140000Z
DTEND;VALUE=DATE-TIME:20210422T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/22
DESCRIPTION:Title: Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-p
reserving dynamical systems\nby Tanja Schindler (Scuola Normale Superi
ore di Pisa (Italy)) as part of DinAmicI: Another Internet Seminar\n\n\nAb
stract\nWe are interested in the limit behaviour of Birkhoff sums over an
infinite sigma-finite measure space. If the observable is integrable then
— by a classical theorem by Aaronson — there exists no sequence of rea
l numbers such that the Birkhoff sum normed by this sequence converges alm
ost surely to 1. Under strong mixing conditions on the underlying system w
e prove a generalized strong law of large numbers for integrable observabl
es using a truncated sum adding a suitable number of terms depending on th
e point of evaluation. For f not integrable we give conditions on f such t
hat the Birkhoff sum normed by a sequence of real numbers converges almost
surely to 1. Joint work with Claudio Bonanno.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selim Ghazouani (Université Paris-Sud (France))
DTSTART;VALUE=DATE-TIME:20210506T140000Z
DTEND;VALUE=DATE-TIME:20210506T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/23
DESCRIPTION:Title: Piecewise affine homeomorphisms of the circle and dilation surfaces\
nby Selim Ghazouani (Université Paris-Sud (France)) as part of DinAmicI:
Another Internet Seminar\n\n\nAbstract\nIn this talk I will consider the f
ollowing question: if one picks a piecewise affine map of the circle “at
random”\, what dynamical behaviour are we likely to observe? The case o
f standard circle diffeomorphisms has been studied by Herman in the 80s\;
in this emblematic case the problem can be reduced to theorems close to KA
M theory. For the piecewise affine case\, we put forward a geometric appro
ach\, inspired by methods from both Teichmüller theory and hyperbolic geo
metry.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa (Italy))
DTSTART;VALUE=DATE-TIME:20210520T140000Z
DTEND;VALUE=DATE-TIME:20210520T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/24
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and diophantine proble
ms in dynamics\nby Umberto Zannier (Scuola Normale Superiore di Pisa (
Italy)) as part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nAfter
a very brief review of basics on elliptic curves and their families\, we
shall consider "sections" of such families\, and especially their "torsio
n values". For instance\, what can be said of the complex numbers b for wh
ich (2\, \\sqrt{2(2-b)}) is torsion on the Legendre curve y^2=x(x-1)(x-b)?
In particular\, we shall recall results of "Manin-Mumford type" and focus
to illustrate some applications to elliptical billiards. Finally\, if tim
e allows we shall frame these issues as special cases of a general questio
n in arithmetic dynamics\, which can be treated with different methods\, d
epending on the context.\n(Most results refer to work with Pietro Corvaja
and David Masser.)\n
LOCATION:https://researchseminars.org/talk/DinAmicI/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tanzi (New York University (USA))
DTSTART;VALUE=DATE-TIME:20210604T140000Z
DTEND;VALUE=DATE-TIME:20210604T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/25
DESCRIPTION:Title: Random-like properties of chaotic forcing\nby Matteo Tanzi (New York
University (USA)) as part of DinAmicI: Another Internet Seminar\n\n\nAbst
ract\nWe prove that skew systems with a sufficiently expanding base have
“approximate” statistical properties similar to random ergodic Markov
chains. For example\, they exhibit approximate exponential decay of correl
ations\, meaning that the exponential rate is observed modulo a controlled
error. The fiber maps are only assumed to be Lipschitz regular and to dep
end on the base in a way that guarantees diffusive behaviour on the vertic
al component. The assumptions do not imply an hyperbolic picture and one c
annot rely on the spectral properties of the transfer operators involved.
The approximate nature of the result is the inevitable price one pays for
having so mild assumptions on the dynamics on the vertical component. The
error in the approximation is shown to go to zero when the expansion of th
e base tends to infinity.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Artigiani (Universidad del Rosario (Colombia))
DTSTART;VALUE=DATE-TIME:20210617T140000Z
DTEND;VALUE=DATE-TIME:20210617T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/26
DESCRIPTION:Title: Double rotations and their ergodic properties\nby Mauro Artigiani (U
niversidad del Rosario (Colombia)) as part of DinAmicI: Another Internet S
eminar\n\n\nAbstract\nDouble rotations are the simplest subclass of interv
al translation mappings. A double rotation is of finite type if its attrac
tor is an interval and of infinite type if it is a Cantor set. It is easy
to see that the restriction of a double rotation of finite type to its att
ractor is simply a rotation. It is known due to Suzuki - Ito - Aihara and
Bruin - Clark that double rotations of infinite type are defined by a subs
et of zero measure in the parameter set. We introduce a new renormalizatio
n procedure on double rotations\, which is reminiscent of the classical Ra
uzy induction. Using this renormalization\, we prove that the set of param
eters which induce infinite type double rotations has Hausdorff dimension
strictly smaller than 3. Moreover\, we construct a natural invariant measu
re supported on these parameters and show that\, with respect to this meas
ure\, almost all double rotations are uniquely ergodic. In my talk I plan
to outline this proof that is based on the recent result by Fougeron for s
implicial systems. I also hope to discuss briefly some challenging open qu
estions and further research plans related to double rotations.\n\nThe tal
k is based on a joint work with Charles Fougeron\, Pascal Hubert and Sasha
Skripchenko.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasun Fernando (University of Toronto (Canada))
DTSTART;VALUE=DATE-TIME:20210624T140000Z
DTEND;VALUE=DATE-TIME:20210624T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T114613Z
UID:DinAmicI/27
DESCRIPTION:Title: Expansions in the mixing local limit theorems for dynamical systems\
nby Kasun Fernando (University of Toronto (Canada)) as part of DinAmicI: A
nother Internet Seminar\n\n\nAbstract\nIn this talk\, we introduce higher-
order expansions in the mixing local limit theorems for Birkhoff sums. We
will discuss the general results under technical assumptions\, and illustr
ate them by different examples (e.g. subshifts of finite type\, Young towe
rs\, Sinai billiards\, and random matrix products)\, including situations
of unbounded observables with integrability order arbitrarily close to the
optimal moment condition required in the i.i.d. setting. This is joint wo
rk with Françoise Pène.\n
LOCATION:https://researchseminars.org/talk/DinAmicI/27/
END:VEVENT
END:VCALENDAR