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BEGIN:VEVENT
SUMMARY:Olga Lukina (University of Vienna)
DTSTART;VALUE=DATE-TIME:20200424T081500Z
DTEND;VALUE=DATE-TIME:20200424T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/1
DESCRIPTION:Title: St
abilizers in group Cantor actions and measures\nby Olga Lukina (Univer
sity of Vienna) as part of Dynamical systems seminar at the Jagiellonian U
niversity\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DSSUJ/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Roth (Silesian University)
DTSTART;VALUE=DATE-TIME:20200515T081500Z
DTEND;VALUE=DATE-TIME:20200515T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/2
DESCRIPTION:Title: Sp
ecial alpha-limit sets on the interval\nby Samuel Roth (Silesian Unive
rsity) as part of Dynamical systems seminar at the Jagiellonian University
\n\nLecture held in 1016.\n\nAbstract\nFor a noninvertible dynamical syste
m (X\,f) a point x can have many\npossible “pasts.” Special alpha limi
t sets were defined to contain all\nthe limit points of all those backward
orbits\, and it turns out that for\ninterval maps they have many good pro
perties. For example\, a point\nbelongs to its own special alpha limit set
(this is like “backward\nrecurrence”) if and only if it is in the att
racting center of the interval\nmap [Hero\, 1992].\n\nOne of the last pape
rs by Sergei Kolyada proposes several conjectures\nand open problems about
topological properties of special-alpha limit\nsets. This talk will addre
ss those problems. The project is joint work\nwith Jana Hantáková.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Kwietniak
DTSTART;VALUE=DATE-TIME:20200508T081500Z
DTEND;VALUE=DATE-TIME:20200508T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/3
DESCRIPTION:Title: En
tropy\, f-bar\, and Abramov's formula for the entropy of induced transform
ations\nby Dominik Kwietniak as part of Dynamical systems seminar at t
he Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nRecall th
at an infinite sequence over a finite alphabet A is\nquasi-regular\, if it
is a generic point for a (non-necessarily\nergodic) shift-invariant measu
re. Given a quasi-regular point x in the\nfull shift over A we write h(x)
for the Kolmogorov-Sinai entropy of\nthe shift invariant Borel probability
measure generated by x. We prove\nthat h is uniformly continuous on the s
et of all quasi-regular points\nendowed with the f-bar (pseudo)distance. W
e also give an alternative\nproof of Abramov's formula for the entropy of
induced transformations.\nThis is a joint work with Tomasz Downarowicz and
Martha Łącka.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Misiurewicz (IUPUI)
DTSTART;VALUE=DATE-TIME:20200522T141500Z
DTEND;VALUE=DATE-TIME:20200522T154500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/4
DESCRIPTION:Title: Fl
exibility of entropies for piecewise expanding unimodal maps\nby Micha
ł Misiurewicz (IUPUI) as part of Dynamical systems seminar at the Jagiell
onian University\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DSSUJ/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Fuhrmann (Imperial College London)
DTSTART;VALUE=DATE-TIME:20200605T081500Z
DTEND;VALUE=DATE-TIME:20200605T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/5
DESCRIPTION:Title: So
me recent progress on tameness in minimal systems\nby Gabriel Fuhrmann
(Imperial College London) as part of Dynamical systems seminar at the Jag
iellonian University\n\nLecture held in 1016.\n\nAbstract\nTameness is a n
otion which--very roughly speaking--refers to the\nabsence of topological
complexity of a dynamical system. The last\ndecades saw an increased inter
est in tame systems revealing their\nconnections to other areas of mathema
tics like Banach spaces\,\nsubstitutions and tilings or even model theory
and logic. In this\ntalk\, we will assume a dynamical systems perspective.
\n\nHuang showed that\, given a minimal system\, tameness implies almost\n
automorphy [1]. That is\, after discarding a meagre set of points\, the\nf
actor map of a tame minimal system to its maximal equicontinuous\nfactor i
s one-to-one. This structural theorem got recently extended to\nactions of
general groups by Glasner [2].\n\nIn a collaboration with Glasner\, Jäge
r and Oertel\, we could further\nimprove this result by showing that tame
minimal systems are actually\nregularly almost automorphic [3]. In this ta
lk\, we will show a closely\nrelated statement which\, however\, is way ea
sier to prove: every\nsymbolic almost automorphic extension of an irration
al rotation whose\nnon-invertible fibres form a Cantor set is non-tame. We
will further\ndiscuss some related results from a collaboration with Kwie
tniak [4].\nFinally\, if time allows\, we will come to discuss tameness in
\nsubstitutive subshifts and more general classes of Toeplitz flows [5].\n
\nAll (non-standard) notions will be introduced in the talk. In other\nwor
ds: we prioritise accessibility over the number of results to be\ndiscusse
d.\n\n[1] W. Huang\, Tame systems and scrambled pairs under an abelian gro
up\naction\, Ergodic Theory Dynam. Systems 26 (2006)\, 1549-1567.\n\n[2] E
. Glasner\, The structure of tame minimal dynamical systems for\ngeneral g
roups\, Invent. Math. 211 (2018)\, 213-244.\n\n[3] G. Fuhrmann\, E. Glasne
r\, T. Jäger\, C. Oertel\, Irregular model sets\nand tame dynamics\, arXi
v:1811.06283\, (2018)\, 1-22.\n\n[4] G. Fuhrmann\, D. Kwietniak\, On tamen
ess of almost automorphic\ndynamical systems for general groups\, Bull. Lo
n. Math. Soc. 52 (2020)\,\n24-42.\n\n[5] G. Fuhrmann\, J. Kellendonk\, R.
Yassawi\, work in progress.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Oertel-Jäger (Friedrich Schiller University Jena)
DTSTART;VALUE=DATE-TIME:20200529T081500Z
DTEND;VALUE=DATE-TIME:20200529T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/6
DESCRIPTION:Title: To
pological dynamics of irregular model sets\nby Tobias Oertel-Jäger (F
riedrich Schiller University Jena) as part of Dynamical systems seminar at
the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nModel s
ets have been introduced by Yves Meyer in 1972. As\nthe underlying cut and
project schemes present a quite general method\nto construct aperiodic po
int-sets with long-range order\, they are\noften studied in the theory of
mathematical quasicrystals. At the same\ntime\, they present an interestin
g class of examples in the context of\ntopological dynamics.\n\nIn this ta
lk\, we will concentrate on the dynamics of so-called\nirregular model set
s\, whose dynamics are generally more complicated\nand less understood tha
n that of regular models (like the Fibonacci\nquasicrystal). We show that
the Delone dynamical systems associated to\nirregular model sets often sho
w positive entropy\, but the construction\nalso allows for uniquely ergodi
c zero entropy examples. However\,\nirregular models sets cannot be tame\,
which provides a lower bound for\nthe complexity of their dynamics.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny (Einstein Institute of Mathematics\, UJ)
DTSTART;VALUE=DATE-TIME:20200612T081500Z
DTEND;VALUE=DATE-TIME:20200612T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/7
DESCRIPTION:Title: Au
tomatic multiplicative sequences\nby Jakub Konieczny (Einstein Institu
te of Mathematics\, UJ) as part of Dynamical systems seminar at the Jagiel
lonian University\n\nLecture held in 1016.\n\nAbstract\nAutomatic sequence
s - that is\, sequences computable by\nfinite automata - give rise to one
of the most basic models of\ncomputation. As such\, for any class of seque
nces it is natural to ask\nwhich sequences in it are automatic. In particu
lar\, the question of\nclassifying automatic multiplicative sequences has
attracted\nconsiderable attention in recent years. In the completely\nmult
iplicative case\, such classification was obtained independently by\nS. Li
and O. Klurman and P. Kurlberg. The main topic of my talk will\nbe the re
solution of the general case\, obtained in a recent preprint\nwith M. Lema
ńczyk and C. Müllner.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Melleray (Institut Camille Jordan\, Université Lyon 1)
DTSTART;VALUE=DATE-TIME:20200619T081500Z
DTEND;VALUE=DATE-TIME:20200619T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/8
DESCRIPTION:Title: Ch
aracterizing sets of invariant probability measures of minimal homeomorphi
sms of the Cantor space\nby Julien Melleray (Institut Camille Jordan\,
Université Lyon 1) as part of Dynamical systems seminar at the Jagiellon
ian University\n\nLecture held in 1016.\n\nAbstract\nGiven a set K of prob
ability measures on a Cantor set X\, one\ncan ask whether there exists a m
inimal homeomorphism (= all orbits are\ndense) whose invariant probability
measures are exactly the elements of\nK. We say that K is a dynamical sim
plex if such a homeomorphism exists\;\nI will present a characterization o
f dynamical simplices\, which is based\nin large part on work of T. Ibarlu
cia and myself\; and try to explain the\nproof strategy\, based on the not
ion of Kakutani-Rokhlin partitions. The\ntalk will be introductory in nat
ure and not assume prior knowledge of\nCantor dynamics.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Kwietniak (Jagiellonian University)
DTSTART;VALUE=DATE-TIME:20201002T081500Z
DTEND;VALUE=DATE-TIME:20201002T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/9
DESCRIPTION:Title: Db
ar-approachability\, entropy density and B-free shifts\nby Dominik Kwi
etniak (Jagiellonian University) as part of Dynamical systems seminar at t
he Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nWe study
which properties of shift spaces transfer to their Hausdorff\nmetric dbar-
limits. In particular\, we study shift spaces we call\ndbar-approachable\,
which are Hausdorff metric dbar-limits of their own\nk-step Markov approx
imations. We provide a topological\ncharacterisation of chain mixing dbar-
approachable shift spaces using\nthe dbar-shadowing property. This can be
considered as an analogue for\nFriedman and Ornstein's characterisation of
Bernoulli processes. We\nprove that many classical specification properti
es imply chain mixing\nand dbar-approachability. It follows that there are
tons of\ninteresting dbar-approachable shift spaces (mixing shifts of fin
ite\ntype\, or more generally mixing sofic shifts\, or even more generally
\,\nshift spaces with the specification or beta-shifts. In addition\, we\n
construct minimal and proximal examples of dbar-approachable shift\nspaces
\, thus proving dbar-approachability is a more general phenomenon\nthan sp
ecification. We also show that dbar-approachability and\nchain-mixing impl
y dbar-stability\, a property recently introduced by\nTim Austin in his st
udy of Bernoulliness of equilibrium states. This\nallows us to provide fir
st examples of minimal or proximal dbar-stable\nshift spaces\, thus answer
ing a question posed by Austin. Finally\, we\nshow that the set of shift
spaces with entropy-dense ergodic measures\nis closed wrt dbar Hausdorff m
etric. Note that entropy-density of\nergodic measures is known to hold for
many classes of shift spaces\nwith variants of the specification property
\, but our result show that\nin these cases the entropy-density is a mere
consequence of\nentropy-density of mixing shifts of finite type and\ndbar-
approachability. Since we know there are examples of minimal or\nproximal
dbar-approachable shifts\, we see that our technique yields\nentropy-densi
ty for examples which were beyond the reach of methods\nbased on specifica
tion properties. Finally\, we apply our technique to\nhereditary closures
of B-free shifts (a class including many\ninteresting B-free shifts). Thes
e shift spaces are not chain-mixing\,\nhence they are not dbar-approachabl
e\, but they are easily seen to be\napproximated by naturally defined sequ
ences of transitive sofic\nshifts\, and this implies entropy-density. This
is a joint work with\nJakub Konieczny and Michal Kupsa.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joanna Kułaga-Przymus (UMK Toruń)
DTSTART;VALUE=DATE-TIME:20201009T081500Z
DTEND;VALUE=DATE-TIME:20201009T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/10
DESCRIPTION:Title: E
ntropy rate of product of independent processes\nby Joanna Kułaga-Prz
ymus (UMK Toruń) as part of Dynamical systems seminar at the Jagiellonian
University\n\nLecture held in 1016.\n\nAbstract\nThe entropy of the produ
ct of stationary processes is related to\nFurstenberg’s filtering proble
m. In its classical version one deals\nwith the sum $\\bm{X}+\\bm{Y}$\, wh
ere $\\bm{X}$ corresponds to the signal\nand $\\bm{Y}$ to the noise. In hi
s seminal paper from 1967\, Furstenberg\nshowed that under the natural ass
umption of the disjointness of\nunderlying dynamical systems\, the informa
tion about $\\bm{X}$ can be\nretrieved from $\\bm{X}+\\bm{Y}$. Instead of
the sum\, we study the\nproduct $\\bm{X}\\cdot\\bm{Y}$. We give a formula
for the entropy rate of\n$\\bm{X}\\cdot\\bm{Y}$ (relative to that of $\\bm
{Y}$\, for $\\bm{X}$ and\n$\\bm{Y}$ being independent). As a consequence\,
$\\bm{X}$ cannot be\nrecovered from $\\bm{X}\\cdot\\bm{Y}$ for a wide cla
ss of positive\nentropy processes\, including exchangeable processes\, Mar
kov chains and\nweakly Bernoulli processes. Moreover\, we answer some open
problems on\nthe dynamics of $\\mathscr{B}$-free systems (including the s
quare-free\nsystem given by the square of the Moebius function). The talk
is based\non joint work with Michał Lemańczyk\, see\nhttps://arxiv.org/p
df/2004.07648.pdf\n
LOCATION:https://researchseminars.org/talk/DSSUJ/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Szczepanek
DTSTART;VALUE=DATE-TIME:20201023T081500Z
DTEND;VALUE=DATE-TIME:20201023T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/11
DESCRIPTION:Title: D
ynamical Entropy of Unitary Operators in Finite-dimensional State Spaces\nby Anna Szczepanek as part of Dynamical systems seminar at the Jagiell
onian University\n\nLecture held in 1016.\n\nAbstract\nQuantum dynamical e
ntropy quantifies the irreducible randomness of the sequences of outcomes
generated by a repetitively measured quantum system that between each two
consecutive measurements is subject to unitary evolution. For several clas
ses of quantum measurements\, we derive an efficient formula for dynamical
entropy by establishing the limiting measure of the Markov chain generate
d by the system and evaluating the Blackwell integral entropy formula. We
also discuss the class of chaotic unitaries\, i.e.\, those with potential
to generate maximally random sequences of outcomes. Employing the notion o
f complex Hadamard matrices\, we give a necessary condition for chaoticity
(expressed in terms of the operator’s trace and determinant)\, which in
dimensions 2 and 3 is sufficient as well.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Byszewski
DTSTART;VALUE=DATE-TIME:20201030T091500Z
DTEND;VALUE=DATE-TIME:20201030T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/12
DESCRIPTION:Title: A
rithmetic properties of the number of periodic points\nby Jakub Byszew
ski as part of Dynamical systems seminar at the Jagiellonian University\n\
nLecture held in 1016.\n\nAbstract\nThe talk will be of expository charact
er and is based on a joint\nsurvey paper with Grzegorz Graff and Thomas Wa
rd. Given a dynamical\nsystem\, we may consider the sequence counting the
number of periodic\npoints of given order (if finite). (Equivalently\, thi
s information can\nbe given in terms of the dynamical zeta function of the
system.) We\nwill discuss some arithmetic properties of the class of sequ
ences that\ncan be obtained in this manner. Many of such results have been
\nindependently rediscovered by various mathematicians working in\nmultipl
e fields.\n\nIn the latter part of the talk\, we will also discuss some mo
re recent\nresults concerning the growth rate of the number of periodic po
ints in\ncertain systems of algebraic origin\, and obtained in a joint wor
k with\nGunther Cornelissen and Marc Houben.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Downarowicz
DTSTART;VALUE=DATE-TIME:20201106T091500Z
DTEND;VALUE=DATE-TIME:20201106T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/13
DESCRIPTION:Title: M
ultiorder of countable groups\nby Tomasz Downarowicz as part of Dynami
cal systems seminar at the Jagiellonian University\n\nLecture held in 1016
.\n\nAbstract\nI will present the notion of a Multiorder of a countable gr
oup\,\na particular case of an Invariant Random Order introduced by\nJohn
Kieffer in 1975.\nI will discuss how multiorder is related to orbit equiva
lence to\nZ-actions and I will prove that if the group is amenable then\ne
ach multiorder has the F\\o lner property. If time permits\, I will\nalso
show how to construct a uniformly F\\o lner multiorder of\nentropy zero\,
using a tiling system.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Hausner (FSU Jena)
DTSTART;VALUE=DATE-TIME:20201127T091500Z
DTEND;VALUE=DATE-TIME:20201127T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/14
DESCRIPTION:Title: E
ntropy in the context of aperiodic order\nby Till Hausner (FSU Jena) a
s part of Dynamical systems seminar at the Jagiellonian University\n\nLect
ure held in 1016.\n\nAbstract\nIn this talk we study different notions of
entropy for\nDelone sets of finite local complexity in the setting of (met
rizable\nand sigma-compact) locally compact Abelian groups (LCA groups).\n
\nFor Delone sets of finite local complexity (FLC) in the euclidean\nspace
it is well known that the patch counting entropy equals the\ntopological
entropy of an associated shift system. We present an\nexample of a FLC Del
one set in a LCA group for which the topological\nentropy and the patch co
unting entropy are not equal.\n\nIt was suggested by J. Lagarias for FLC D
elone sets in the euclidean\nspace that the patch counting entropy can alw
ays be computed as a\nlimit. We discuss why the Ornstein-Weiss lemma can n
ot directly be\nused in order to see this claim and present that the corre
spondence\nbetween the topological and the patch counting entropy can be u
sed in\norder to show that the limit in the patch counting entropy formula
\nexists for compactly generated LCA groups. We present counterexamples\nw
here the limit does not exist in the context of general LCA groups.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paulo Varandas (UFBA/Porto)
DTSTART;VALUE=DATE-TIME:20201120T091500Z
DTEND;VALUE=DATE-TIME:20201120T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/15
DESCRIPTION:Title: P
hase transitions and appearance of ghost measures\nby Paulo Varandas (
UFBA/Porto) as part of Dynamical systems seminar at the Jagiellonian Unive
rsity\n\nLecture held in 1016.\n\nAbstract\nThe thermodynamic formalism fo
r transitive uniformly\nhyperbolic dynamics is nowadays well understood an
d\, among other\naspects\, it is worth mentioning that regular potentials
(meaning\nHolder continuous) are so that the pressure function is differen
tiable\nand admit unique equilibrium states. The situation changes drastic
ally\nin simple examples beyond uniform hyperbolicity\, as the case of the
\nManneville-Pomeau maps\, where different kinds of phase transitions\napp
ear due to the phenomenon of intermittency of an indifferent fixed\npoint.
In this talk I will focus on this family and discuss a new\naspect of the
phase transitions\, namely the appearance of finitely\nadditive absolutel
y continuous invariant measures.In particular\, the\nsecond-order phase tr
ansition can be detected as a first-order phase\ntransition for an extende
d pressure function. This is part of an\nongoing work with A. Castro (UFBA
) and L. Cioletti (UnB).\n
LOCATION:https://researchseminars.org/talk/DSSUJ/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Wolf (CUNY)
DTSTART;VALUE=DATE-TIME:20201204T140000Z
DTEND;VALUE=DATE-TIME:20201204T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/16
DESCRIPTION:Title: C
omputability of topological pressure on compact shift spaces beyond finite
type\nby Christian Wolf (CUNY) as part of Dynamical systems seminar a
t the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nIn thi
s talk we discuss the computability (in the sense of computable\nanalysis)
of the topological pressure $P_{\\rm top}(\\phi)$ on compact\nshift space
s $X$ for continuous potentials $\\phi:X\\to\\bR$. This\nquestion has rece
ntly been studied for subshifts of finite type (SFTs)\nand their factors (
Sofic shifts). We develop a framework to address\nthe computability of the
topological pressure on general shift spaces\nand apply this framework to
coded shifts. In particular\, we prove the\ncomputability of the topologi
cal pressure for all continuous\npotentials on S-gap shifts\, generalized
gap shifts\, and Beta shifts.\nWe also construct shift spaces which\, depe
nding on the potential\,\nexhibit computability and non-computability of t
he topological\npressure. We further show that the generalized pressure fu
nction\n$(X\,\\phi)\\mapsto P_{\\rm top}(X\,\\phi\\vert_{X})$ is not compu
table for a\nlarge set of shift spaces $X$ and potentials $\\phi$. Along t
he way of\ndeveloping these computability results\, we derive several\nerg
odic-theoretical properties of coded shifts which are of\nindependent inte
rest beyond the realm of computability. The topic of\nthe talk is joint wo
rk with Michael Burr (Clemson U.)\, Shuddho Das\n(NYU) and Yun Yang (Virgi
nia Tech).\n
LOCATION:https://researchseminars.org/talk/DSSUJ/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Todd (St. Andrews)
DTSTART;VALUE=DATE-TIME:20201211T091500Z
DTEND;VALUE=DATE-TIME:20201211T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/17
DESCRIPTION:Title: P
ressure on non-compact spaces\nby Mike Todd (St. Andrews) as part of D
ynamical systems seminar at the Jagiellonian University\n\nLecture held in
1016.\n\nAbstract\nThermodynamic formalism has a lot to say in the contex
t of\nsufficiently regular dynamical systems in compact spaces\, for examp
le\nabout the existence and uniqueness properties of equilibrium states\,\
nand their characterisation as some derivative of the pressure\nfunction.
This talk considers non-compact settings\, particularly the\ncase of coun
table Markov shifts. A first natural approach is to take\nthe completion
of the space and hope that the boundary created doesn’t\ninterfere with
too many thermodynamic properties. I’ll look at how\none might do this\
, some drawbacks\, and how they can\, in some cases\, be\novercome.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katrin Gelfert (UFRJ)
DTSTART;VALUE=DATE-TIME:20201113T101500Z
DTEND;VALUE=DATE-TIME:20201113T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/18
DESCRIPTION:Title: H
eterodimensionality of skew-products with concave fiber maps\nby Katri
n Gelfert (UFRJ) as part of Dynamical systems seminar at the Jagiellonian
University\n\nLecture held in 1016.\n\nAbstract\nI will present some examp
les of skew-products with concave\ninterval fiber maps over a certain subs
hift. Here the subshift occurs\nas the projection of those orbits that sta
y in a given neighborhood\nand gives rise to a new type of symbolic space
which is (essentially)\ncoded. The fiber maps have expanding and contracti
ng regions. As a\nconsequence\, the skew-product dynamics has pairs of hor
seshoes of\ndifferent type of hyperbolicity. In some cases\, they dynamica
lly\ninteract due to the superimposed effects of the (fiber) contraction\n
and expansion\, leading to nonhyperbolic dynamics that is reflected on\nth
e ergodic level (existence of nonhyperbolic ergodic measures). The\nspace
of ergodic measures of the shift space is shown to be an\nentropy-dense Po
ulsen simplex\, ergodic measures lift canonically to\nergodic measures for
the skew-product.\nSuch skew-products can be embedded in increasing entro
py one-parameter\nfamily of diffeomorphisms which stretch from a heterodim
ensional cycle\nto a collision of homoclinic classes. I will discuss some
ingredients\nof associated bifurcation phenomena that involve a jump of th
e space\nof ergodic measures and\, in some cases\, also of entropy. (Joint
work\nwith L.J.Díaz and M.Rams)\n
LOCATION:https://researchseminars.org/talk/DSSUJ/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Mroczek
DTSTART;VALUE=DATE-TIME:20210108T091500Z
DTEND;VALUE=DATE-TIME:20210108T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/19
DESCRIPTION:Title: T
he Besicovitch Metric on the Space of G -invariant Ergodic Measures\nb
y Marcel Mroczek as part of Dynamical systems seminar at the Jagiellonian
University\n\nLecture held in 1016.\n\nAbstract\nGiven two sequences over
a finite alphabet\, one can measure the distance between them by looking h
ow their asymptotic behaviours differ. This gives rise to dynamically gene
rated Besicovitch pseudometric. I will talk about the generalisation of th
is concept to actions of countable amenable groups. I will show that it in
duces a metric on the space of ergodic measures invariant under the action
\, and that in the case of the shift space\, entropy function is continuou
s with respect to this metric. As an application of these results\, I will
show that if the considered group is in addition residually finite\, then
uniquely ergodic measures are entropy dense in the set of totally ergodic
measures. This is a joint work with Martha Łącka.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Boroński
DTSTART;VALUE=DATE-TIME:20210122T091500Z
DTEND;VALUE=DATE-TIME:20210122T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/20
DESCRIPTION:Title: P
arametric families of attractors and inverse limits\nby Jan Boroński
as part of Dynamical systems seminar at the Jagiellonian University\n\nLec
ture held in 1016.\n\nAbstract\nIn my talk I shall discuss some of my rece
nt work on\nparametric families of maps and their strange attractors on su
rfaces\,\nwhich employed inverse limit approach. They were focusing on com
puting\naccessible rotation numbers (e.g. for reduced Arnold Standard Fami
ly\n[1])\, and building 1-dimensional models that are reductions of\n2-dim
ensional dynamics in the presence of strong (mild) dissipation\n[2]. The l
atter was inspired by recent results of Crovisier and Pujals\n[3] (see als
o [4]).\n\nReferences\n[1] Boroński\, J. P.\; Činč\, J.\; Liu\, X-C "Pr
ime ends dynamics in\nparametrised families of rotational attractors". J.
Lond. Math. Soc.\n(2) 102 (2020)\, no. 2\, 557–579.\n[2] Topological and
Smooth Dynamics on Surfaces\, Mathematisches\nForschungsinstitut Oberwolf
ach Report No. 27/2020\, DOI:\n10.4171/OWR/2020/27\n[3] S. Crovisier\, E.
Pujals\, "Strongly dissipative surface\ndiffeomorphisms"\, Commentarii Mat
hematici Helvetici 93 (2018)\,\n377–400.\n[4] S. Crovisier\, E. Pujals\,
C\, Tresser\, "Mild dissipative\ndiffeomorphisms of the disk with zero en
tropy"\, arXiv 2020.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sascha Troscheit
DTSTART;VALUE=DATE-TIME:20210305T091500Z
DTEND;VALUE=DATE-TIME:20210305T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/21
DESCRIPTION:Title: A
dimension theory approach to embeddings in random geometry\nby Sascha
Troscheit as part of Dynamical systems seminar at the Jagiellonian Univer
sity\n\nLecture held in 1016.\n\nAbstract\nThe continuum random tree and B
rownian map are important\nmetric spaces in probability theory and represe
nt the "typical" tree\nand metric on the sphere\, respectively. The Browni
an map in particular\nis linked to Liouville Quantum Gravity but the exact
nature of the\ncorrespondence is unknown.\nIn this talk I will explain a
fairly dynamical construction of these\nspaces and show how recent advance
s in the dimension theory of\nself-similar sets can be used to shed light
on general embedding\nproblems. In particular\, I will show that the Assou
ad dimension of\nthese metric spaces is infinite and show how this restric
ts the nature\nof embeddings. Time permitting\, I will also indicate how t
he\nconstruction of continuum trees may be used to analyse highly singular
\nfunctions such as the Weierstrass-type functions.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurelia Bartnicka
DTSTART;VALUE=DATE-TIME:20210326T091500Z
DTEND;VALUE=DATE-TIME:20210326T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/22
DESCRIPTION:Title: T
opological dynamics of multidimensional $\\mathscr{B}$-free systems: proxi
mality\, minimality and maximal equicontinuous factor.\nby Aurelia Bar
tnicka as part of Dynamical systems seminar at the Jagiellonian University
\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DSSUJ/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Barge
DTSTART;VALUE=DATE-TIME:20210409T081500Z
DTEND;VALUE=DATE-TIME:20210409T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/23
DESCRIPTION:by Hector Barge as part of Dynamical systems seminar at the Ja
giellonian University\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DSSUJ/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny
DTSTART;VALUE=DATE-TIME:20210312T091500Z
DTEND;VALUE=DATE-TIME:20210312T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/24
DESCRIPTION:Title: Q
uasicrystals from the point of view of additive combinatorics\nby Jaku
b Konieczny as part of Dynamical systems seminar at the Jagiellonian Unive
rsity\n\nLecture held in 1016.\n\nAbstract\nWe show that some results in a
dditive combinatorics can\nbe translated into corresponding results that a
re relevant to the\nmathematical theory of quasicrystals. Specifically\, w
e will use the\nFreiman–Ruzsa theorem\, characterising finite sets with
bounded\ndoubling\, to obtain an alternative proof of a characterisation o
f\nMeyer sets\, that is\, relatively dense subsets of Euclidean spaces\nwh
ose difference sets are uniformly discrete.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maik Gröger
DTSTART;VALUE=DATE-TIME:20210319T091500Z
DTEND;VALUE=DATE-TIME:20210319T104500Z
DTSTAMP;VALUE=DATE-TIME:20210419T091145Z
UID:DSSUJ/25
DESCRIPTION:Title: G
roup actions with discrete spectrum and their amorphic complexity\nby
Maik Gröger as part of Dynamical systems seminar at the Jagiellonian Univ
ersity\n\nLecture held in 1016.\n\nAbstract\nAmorphic complexity\, origina
lly introduced for integer actions\, is a\ntopological invariant which mea
sures the complexity of dynamical\nsystems in the regime of zero entropy.\
nWe will explain its definition for actions by locally compact\nsigma-comp
act amenable groups on compact metric spaces.\nAfterwards\, we will illust
rate some of its basic properties and show\nwhy it is tailor-made to study
strictly ergodic group actions with\ndiscrete spectrum and continuous eig
enfunctions.\nThis class of actions includes\, in particular\, Delone dyna
mical\nsystems related to regular model sets obtained via cut and project\
nschemes (CPS).\nFinally\, for this family of Delone dynamical systems we
present sharp\nupper bounds on amorphic complexity utilizing basic propert
ies of the\ncorresponding CPS.\nThis is joint work with G. Fuhrmann\, T. J
äger and D. Kwietniak.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/25/
END:VEVENT
END:VCALENDAR