BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Olga Lukina (University of Vienna) DTSTART:20200424T081500Z DTEND:20200424T094500Z DTSTAMP:20260422T225827Z 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:20200515T081500Z DTEND:20200515T094500Z DTSTAMP:20260422T225827Z 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:20200508T081500Z DTEND:20200508T094500Z DTSTAMP:20260422T225827Z 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:20200522T141500Z DTEND:20200522T154500Z DTSTAMP:20260422T225827Z 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:20200605T081500Z DTEND:20200605T094500Z DTSTAMP:20260422T225827Z 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:20200529T081500Z DTEND:20200529T094500Z DTSTAMP:20260422T225827Z 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:20200612T081500Z DTEND:20200612T094500Z DTSTAMP:20260422T225827Z 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:20200619T081500Z DTEND:20200619T094500Z DTSTAMP:20260422T225827Z 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:20201002T081500Z DTEND:20201002T094500Z DTSTAMP:20260422T225827Z 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:20201009T081500Z DTEND:20201009T094500Z DTSTAMP:20260422T225827Z 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:20201023T081500Z DTEND:20201023T094500Z DTSTAMP:20260422T225827Z 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:20201030T091500Z DTEND:20201030T104500Z DTSTAMP:20260422T225827Z 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:20201106T091500Z DTEND:20201106T104500Z DTSTAMP:20260422T225827Z 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:20201127T091500Z DTEND:20201127T104500Z DTSTAMP:20260422T225827Z 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:20201120T091500Z DTEND:20201120T104500Z DTSTAMP:20260422T225827Z 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:20201204T140000Z DTEND:20201204T150000Z DTSTAMP:20260422T225827Z 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:20201211T091500Z DTEND:20201211T104500Z DTSTAMP:20260422T225827Z 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:20201113T101500Z DTEND:20201113T104500Z DTSTAMP:20260422T225827Z 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:20210108T091500Z DTEND:20210108T104500Z DTSTAMP:20260422T225827Z 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:20210122T091500Z DTEND:20210122T104500Z DTSTAMP:20260422T225827Z 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:20210305T091500Z DTEND:20210305T104500Z DTSTAMP:20260422T225827Z 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:20210326T091500Z DTEND:20210326T104500Z DTSTAMP:20260422T225827Z 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:20210409T081500Z DTEND:20210409T094500Z DTSTAMP:20260422T225827Z 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:20210312T091500Z DTEND:20210312T104500Z DTSTAMP:20260422T225827Z 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:20210319T091500Z DTEND:20210319T104500Z DTSTAMP:20260422T225827Z 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 BEGIN:VEVENT SUMMARY:Thiago Raszeja (University of São Paulo (USP)\, Brazil) DTSTART:20210428T131500Z DTEND:20210428T144500Z DTSTAMP:20260422T225827Z UID:DSSUJ/26 DESCRIPTION:Title: T hermodynamic formalism on generalized countable Markov shifts\nby Thia go Raszeja (University of São Paulo (USP)\, Brazil) as part of Dynamical systems seminar at the Jagiellonian University\n\nLecture held in 1016.\n\ nAbstract\nGiven a 0-1 infinite matrix $A$\, R. Exel and M. Laca have\nint roduced a kind of \\textit{generalized countable Markov shift}\n(GCMS) $X_ A=\\Sigma_A \\cup Y_A$\, which is a locally compact (in many\nimportant ca ses compact) version of $\\Sigma_A$\, the standard countable\nMarkov shift . The elements of $Y_A$ are finite words\, possibly\nincluding multiplicit ies. We develop the thermodynamic formalism for\nGCMS\, where we introduce d the notion of conformal measure on $X_A$\,\nand we explored its connecti ons with the usual formalism on\n$\\Sigma_A$. Among the results\, we highl ight the finding of new\nconformal measures that are not detected by the t hermodynamic\nformalism on $\\Sigma_A$ and new phase transition phenomena: for a wide\nclass of GCMS and potentials\, we determined regions for the inverse of\nthe temperature $\\beta$\, where we absence\\existence of thes e new\nconformal probabilities\, living on $Y_A$. The Gurevich entropy $h_ G$\nplays a fundamental role in determining these regions since the\ncriti cal value for gauge potentials is $h_G$ when finite. We also have\nphase t ransition results for $h_G = \\infty$\, including the full shift.\nIn addi tion\, for the eigenmeasures of Ruelle's transformation\, we\ndiscovered a length-type phase transition in the renewal shift: the\nexistence of a cr itical value for $\\beta$ where the measure passes\nfrom living on $\\Sigm a_A$ to live on $Y_A$. We showed that the notion\nof pressure introduced b y M. Denker and M. Yuri for Iterated Function\nSystems (IFS) is a natural definition of pressure for $X_A$\, and it\ncoincides with the Gurevich pre ssure for GCMS basically for the same\ngenerality on which the thermodynam ic formalism is developed for the\nstandard countable Markov shifts and po tentials.\n\nJoint work with R. Bissacot (University of São Paulo (USP)\, Brazil)\,\nR. Exel (Federal University of Santa Catarina (UFSC)\, Brazil) \, and R.\nFrausino (University of Wollongong (UOW)\, Australia).\n LOCATION:https://researchseminars.org/talk/DSSUJ/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Elżbieta Krawczyk (Jagiellonian University) DTSTART:20210507T081500Z DTEND:20210507T094500Z DTSTAMP:20260422T225827Z UID:DSSUJ/27 DESCRIPTION:Title: A utomatic sequences in automatic systems\nby Elżbieta Krawczyk (Jagiel lonian University) as part of Dynamical systems seminar at the Jagiellonia n University\n\nLecture held in 1016.\n\nAbstract\nA sequence is called au tomatic if it can be obtained as a coding of a fixed point of a substituti on of constant length. We study the class of automatic systems\, that is s ystems which arise as orbit closures of automatic sequences. \n\nSince the re are only countably many automatic sequences\, and since automatic syste ms usually have uncountably many points\, it is interesting to study the c ombinatorial structure of the subset of an automatic system which comprise s all of its points which are automatic. We give a dynamical description o f this set\, which is analogous to the one obtained by Holton and Zamboni for minimal substitutive systems. In particular\, we show that automatic s equences in an infinite minimal automatic system correspond to the rationa ls in the ring of k-adic integers\, the maximal connected equicontinuous f actor of the system. \n\n As an application\, we show that any minimal sub stitutive system which factors onto an infinite k-automatic system is itse lf k-automatic. We also state several conjectures which generalise our res ults to arbitrary substitutive systems\, and explain their relation to Cob ham-type results (connected with the ones obtained by Durand in 2011).\n LOCATION:https://researchseminars.org/talk/DSSUJ/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Trilles (Jagiellonian University) DTSTART:20210514T081500Z DTEND:20210514T094500Z DTSTAMP:20260422T225827Z UID:DSSUJ/28 DESCRIPTION:Title: T opological stability of iterated function systems\nby Alexandre Trille s (Jagiellonian University) as part of Dynamical systems seminar at the Ja giellonian University\n\nLecture held in 1016.\n\nAbstract\nWe study Itera ted Function Systems (IFS) with compact parameter space.\nWe show that the compactness of the phase space permits us to obtain a natural metric\non the space of IFS which extends $C^0$-topology to the space of IFS.\nWe the n use this metric to define topological stability and to prove that\nin th is context the classical results saying that shadowing property is a neces sary\ncondition for topological stability and that shadowing property toge ther\nwith expansiveness are sufficient conditions.\n\nFor a proof of thes e statements\, in fact we use a stronger type of shadowing property\nwhich we show to be different than the standard one.\n\nThis is joint work with Alexander Arbieto.\n LOCATION:https://researchseminars.org/talk/DSSUJ/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Stadlbauer (Universidade Federal do Rio de Janeiro) DTSTART:20210521T081500Z DTEND:20210521T094500Z DTSTAMP:20260422T225827Z UID:DSSUJ/29 DESCRIPTION:Title: A logarithmic law for continued fractions with sequentially restricted entr ies\nby Manuel Stadlbauer (Universidade Federal do Rio de Janeiro) as part of Dynamical systems seminar at the Jagiellonian University\n\n\nAbst ract\nNon-stationary shift spaces are basic models of sequential dynamical system who were intensively studied in order to construct symbolic models for ergodic automorphism (Vershik) or in the context of the isomorphism p roblem of shift spaces (Krieger). Recently\, the focus moved towards therm odynamic formalism and related questions. A fundamental tool of thermodyna mic formalism\, Ruelle's operator theorem\, has no immediate generalizatio n to the non-stationary setting as invariant functions intrinsically may n ot exist. However\, it is possible to establish geometric ergodicity for a family of ratios of operators. \n\nThis approach has applications to a cl assical problem in metric number theory. For a sequence $(\\alpha_n)$ conv erging to $\\infty$\, set \n\\[X_\\alpha := \\left\\{ x = \\frac{1}{x_1 + \\frac{1}{x_2 + \\cdots} } : x_n \\in \\mathbb N\, x_n \\geq \\alpha_n \ \hbox{ for all } n \\right\\}.\\] \nThat is\, $X$ is the subset of $[0\,1] $ such that the $n$-th entry of the continued fraction expansion of each element is bigger than or equal to $\\alpha_n$. In this setting\, for $\\a lpha_n \\gg n^{1+\\epsilon}$\, the geometric ergodicity implies a law of the iterated logarithm for square integrable functions from geometric ergo dicity. If\, in addition\, $(\\alpha_n)$ does not behave too wildly\, the reference measure is absolutely contiunous with respect to the Hausdorff m easure (and the Hausdorff dimension is $1/2$). \\\\\n LOCATION:https://researchseminars.org/talk/DSSUJ/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Lemańczyk (University of Warsaw) DTSTART:20211203T091500Z DTEND:20211203T104500Z DTSTAMP:20260422T225827Z UID:DSSUJ/30 DESCRIPTION:Title: T opological pressure of convolution systems with application to B-free syst ems\nby Michał Lemańczyk (University of Warsaw) as part of Dynamical systems seminar at the Jagiellonian University\n\nLecture held in 1016.\n \nAbstract\nI will introduce the notion of a convolution system and show f ormulas\nfor the topological pressure in this setting. As an application\, I\nwill give a plain formula for the topological pressure for the\nheredi tary closure of any B-free system (for an arbitrary continuous\npotential) . The talk will be based on joint paper with Joanna\nKułaga-Przymus.\n LOCATION:https://researchseminars.org/talk/DSSUJ/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Antoine Guihéneuf (Sorbonne Université) DTSTART:20211210T091500Z DTEND:20211210T104500Z DTSTAMP:20260422T225827Z UID:DSSUJ/31 DESCRIPTION:Title: T wo examples of systems with historic behaviour\nby Pierre-Antoine Guih éneuf (Sorbonne Université) as part of Dynamical systems seminar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nA system is said to have historic behaviour if there is a\npositive Lebesgue measure s et of points having non convergent Birkhoff\naverages. The question of kno wing whether systems with historic\nbehaviour are abundant in some familie s of dynamics has recently\nregained attention\, with the recent works of Kiriki and Soma\, and\nBerger's definition of (local) emergence\, which me asures how big is the\nset of accumulation points of Birkhoff averages.\n\ nIn this talk\, I will present two examples of systems with historic\nbeha viour.\n\nThe first one\, obtained with Guarino and Santiago\, is a modifi cation of\nBowen's eye example in which the set of points with historic be haviour\nis of positive Lebesgue measure but nowhere dense.\n\nThe second one\, in collaboration with Andersson\, is the study of\nreparametrized li near flows of the two torus with two fixed points\; we\nobtain some Diopha ntine conditions on the flow's parameters under which\nthe system has/has not historic behaviour.\n LOCATION:https://researchseminars.org/talk/DSSUJ/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Kanigowski (University of Maryland) DTSTART:20220311T151500Z DTEND:20220311T164500Z DTSTAMP:20260422T225827Z UID:DSSUJ/32 DESCRIPTION:Title: E rgodic and statistical properties of smooth systems\nby Adam Kanigowsk i (University of Maryland) as part of Dynamical systems seminar at the Jag iellonian University\n\nLecture held in 1016.\n\nAbstract\nWe will discuss some classical ergodic (Bernoulli\, K-property\, positive entropy...) and statistical (limit theorems\, quantitative mixing...) properties of smoot h dynamical systems. We will discuss their flexibility (i.e. non-trivial e xamples of systems which satisfy some but not all of them) and rigidity (i .e. some properties imply other). We will mostly focus on two results: 1) exponential mixing implies Bernoulli 2) existence of zero entropy systems satisfying a central limit theorem.\n LOCATION:https://researchseminars.org/talk/DSSUJ/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Sohail Farhangi (Ohio State University) DTSTART:20220318T150000Z DTEND:20220318T164500Z DTSTAMP:20260422T225827Z UID:DSSUJ/33 DESCRIPTION:Title: E nhancements of van der Corput's Difference Theorem and connections to the ergodic hierarchy of mixing.\nby Sohail Farhangi (Ohio State Universit y) as part of Dynamical systems seminar at the Jagiellonian University\n\n Lecture held in 1016.\n\nAbstract\nWe will examine three commonly used var iants of van der\nCorput's Difference Theorem (vdCDT) in Hilbert spaces an d show that\nthey are associated with the notions of weak mixing\, strong mixing\,\nand Bernoullicity. We will then use this association to derive 2 new\nvdCDTs corresponding to ergodicity and mild mixing. We remark that\ nour methods naturally yield vdCDTs for a class of unbounded sequences\nof vectors. We will then obtain an application to recurrence in\nmeasure pre serving systems by giving a partial answer to a question of\nFrantzikinaki s. If time permits\, we will also discuss analogues of\nthese vdCDTs in th e context of uniform distribution and the classes of\n"mixing distribution s" that they produce.\n LOCATION:https://researchseminars.org/talk/DSSUJ/33/ END:VEVENT END:VCALENDAR