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Book of Abstracts International conference held online at UniwersytetL´odzki, L´od´z,Poland BOOK OF ABSTRACTS 1 Dynamics of (Semi{)Group Actions The modern theory of dynamical systems encompasses the study of group and semi-group actions, which include vibrant, exciting, and very active lines of research. The primary aim of the conference is to bring together mathematicians involved in topological, mea- surable and algebraic aspects of dynamical systems generated by (semi-)group actions, to stimulate the exchange of new ideas and to offer new opportunities for broadening scientific contacts. This is reflected by the inclusion of young and experienced researchers giving plenary talks and contributed talks. The scope of this conference encompasses research of the dynamical, geometric and algebraic aspects of semi-group actions by continuous mappings of real or complex variables. The wide range of topics include thermodynamic formalism for random dynamical systems, fractal dimension of self-similar sets, entropy and pressure functionals for semigroup actions, topological and ergodic aspects of algebraic actions, among many others. This is the second edition of the conference (the first one took place inL´od´zon 2019). We wish you a pleasant and fruitful (even if online) participation. Organizers 2 Organizers Scientific Committee Andrzej Bi´s(UniwersytetL´odzki,Poland) Dikran Dikranjan (Universit`adegli Studi di Udine, Italy) Tomasz Downarowicz (Politechnika Wroc lawska, Poland) Lubomir Snoha (Univerzita Mateja Bela, Slovakia) Luchezar Stoyanov (University of Western Australia, Australia) Mariusz Urba´nski(University of North Texas, USA) Paulo Varandas (Universidade Federal da Bahia, Brazil; Universidade do Porto, Portugal) Organizing Committee Andrzej Bi´s(UniwersytetL´odzki)| chairman Kamil Niedzia lomski(UniwersytetL´odzki)| secretary Marek Badura (UniwersytetL´odzki) Adam Bartoszek (UniwersytetL´odzki) Magorzata Ciska{Niedzia lomska (UniwersytetL´odzki) Maciej Czarnecki (UniwersytetL´odzki) Yonatan Gutman (Instytut Matematyczny Polskiej Akademii Nauk) Marzena Jaworska-Banert (UniwersytetL´odzki) Wojciech Koz lowski (UniwersytetL´odzki) Ryszard Pawlak (UniwersytetL´odzki) Sponsors UniwersytetL´odzki Wydzia lMatematyki i Informatyki UniwersytetuL´odzkiego 3 Schedule Hours of talks in the European summer time (UTC+2) Tuesday, June 22 09:50 { 10:00 Opening 10:00 { 10:50 Mark Pollicott, Rate of escape for random walks on SL(2; R) 11:00 { 11:50 Micha lRams, Restricted variational principle for partially hyperbolic dynamics 12:00 { 12:30 coffee break 12:30 { 12:55 Antongiulio Fornasiero, Algebraic entropy and Hilbert polynomials 13:00 { 13:25 Jose C´anovas, On two notions of fuzzy topological entropy 13:30 { 13:55 Andrei Tetenov, Three theorems on self-similar continua with finite intersection property 14:00 { 16:00 lunch break 16:00 { 16:50 Maria Carvalho, Generalized entropy maps, variational principles and equilibrium states 17:00 { 17:50 Eugen Mihailescu, Pressure functionals in semigroup dynamics 18:00 { 18:25 Ryszard Pawlak, On points of distributive chaos 18:30 { 18:55 Jason Atnip, Thermodynamic formalism for random interval maps with holes Wednesday, June 23 10:00 { 10:50 Eli Glasner, Topological characteristic factors and nilsystems 11:00 { 11:50 Alexander Bufetov, Determinantal point processes: quasi-symmetries and interpolation 12:00 { 12:30 coffee break 12:30 { 12:55 Nikolai Edeko, A dynamical proof of the van der Corput inequality 13:00 { 13:25 Lubomir Snoha, Product of minimal spaces: complete solution 13:30 { 13:55 Everaldo de Mello Bonotto, Global attractors for semigroups under impulse action 14:00 { 16:00 lunch break 16:00 { 16:50 Vitaly Bergelson, Dynamics actions of (N; ×) 17:00 { 17:50 Vadim Kaimanovich, Coincidence, equivalence and singularity of harmonic measures 18:00 { 18:25 Henrik Kreidler, The Furstenberg-Zimmer structure theorem revisited 18:30 { 18:55 Konstantin Slutsky, L1 full groups of measure-preservingactions of Polish normed groups 4 Thursday, June 24 10:00 { 10:25 Takatyuki Watanabe, Non-i.i.d. random holomorphic dynamical systems 10:30 { 10:55 Johannes Jaerisch, Hausdorff dimension of escaping sets for Z-extensions of expanding interval maps 11:00 { 11:25 Andrzej Bi´s, Topological entropy, upper Carath´eodory capacity and fractal dimensions of semi- group actions 11:30 { 11:55 Till Hauser, Entropy beyond actions of uniform lattices 12:00 { 12:30 coffee break 12:30 { 12:55 Yuto Nakajima, The Hausdorff dimension of some planar sets with unbounded digits 13:00 { 13:50 Manuel Stadlbauer, Equilibrium states associated with the joint action of Ruelle expanding maps 14:00 { 16:00 lunch break 16:00 { 16:50 Anna Giordano Bruno, Receptive topological and metric entropy 17:00 { 17:50 Tom Ward, Order of mixing in algebraic systems 18:00 { 18:25 Mariusz Urba´nski, Random non-hyperbolic exponential maps 18:30 { 18:55 Mauricio D´ıaz, Levels of local chaos for special Blocks Families Friday, June 25 10:00 { 10:50 Hiroki Sumi, Random dynamical systems of regular polynomial maps on C2 11:00 { 11:50 Benjamin Weiss, The Foias-Stratila theorem in higher dimensions 12:00 { 12:30 coffee break 12:30 { 12:55 Oleg Gutik, On some generalization of the bicyclic monoid 13:00 { 13:25 Adam Spiewak,´ Singular stationary measures for random piecewise affine interval homeomor- phisms 13:30 { 15:30 lunch break 15:30 { 16:20 Raimundo Brice~no, Kieffer–Pinsker type formulas for Gibbs measures 16:30 { 17:20 Feliks Przytycki, On Hausdorff dimension of polynomial not totally disconnected Julia sets 17:30 { 17:45 Closing 5 Abstracts Tuesday, June 22, 18:30-18:55 Jason Atnip University of South Wales, Australia [email protected] Thermodynamic formalism for random interval maps with holes In this talk we will consider a collection of piecewise monotone interval maps, which we iterate randomly, together with a collection of holes placed randomly throughout phase space. Birkhoffs Ergodic Theorem implies that the trajec- tory of almost every point will eventually land in one of these holes. We prove the existence of an absolutely continuous conditionally invariant measure, conditioned according to survival from the infinite past. Absolute continuity is with respect to a conformal measure on the closed systems without holes. Furthermore, we prove that the rate at which mass escapes from phase space is equal to the difference in the expected pressures of the closed and open systems. Finally, we prove a formula for the Hausdorff dimension of the fractal set of points whose trajectories never land in a hole in terms of the expected pressure function. ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Wednesday, June 23, 16:00-16:50 Vitaly Bergelson Ohio State University, USA [email protected] Dynamics of actions of (N; ×) We will present several examples of actions of the multiplicative semigroup (N; ×) and discuss some interesting applications to Ramsey theory and Diophantine approximations. We will also discuss and juxtapose combinatorial and Diophantine properties of normal sets in semigroups (N; +) and (N; ×). We will conclude with a brief review of some interesting open problems. ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Thursday, June 24, 11:00-11:25 Andrzej Bi´s UniwersytetL´odzki,Poland [email protected] Topologigal entropy, upper Carath´eodory capacity and fractal dimensions of semigroup actions We study dynamical systems given by the action T : G × X ! X of a finitely generated semigroup G with identity 1 on a compact metric space X by continuous selfmaps . For any finite generating set G1 of G, the receptive topological entropy of G1 (in the sense of Ghys et al. (1988) and Hofmann and Stoyanov (1995)) is shown to coincide with the limit of upper capacities of dynamically defined Carath´eodory structures on X depending on G1, and a similar result holds 6 true for the classical topological entropy when G is amenable. Moreover, the receptive topological entropy and the topological entropy of G1 are lower bounded by respective generalizations of Katoks δ{measure entropy, for δ 2 (0; 1). In the case when T (g; −) is a locally expanding selfmap of X for every g 2 G n f1g, we show that the receptive topological entropy of G1 dominates the Hausdorff dimension of X modulo a factor log λ determined by the expanding coefficients of the elements of fT (g; −): g 2 G1 n f1gg. The talk is based on joint work with Dikran Dikranjan (Udine), Anna Giordano Bruno (Udine) and Luchezar Stoyanov (Perth). ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Wednesday, June 23, 13:30-13:55 Everaldo de Mello Bonotto Universidade de S~aoPaulo, Brazil [email protected] Global attractors for semigroups under impulse action Impulsive semidynamical systems are used to describe the evolution of processes whose continuous dynamics are interrupted by abrupt changes of state. In this talk, we present the theory of impulsive semidynamical systems and we exhibit the definition of global attractors for this class of impulsive systems. Sufficient conditions are presented to guarantee the existence of a global attractor. [1] E. M. Bonotto; M. C. Bortolan; A. N. Carvalho; R. Czaja, Global attractors for impulsive dynamical systems { a precompact approach, Journal of Differential Equations, 2602-2625, 2015. ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Friday, June 25, 15:30{16:20 Raimundo Brice~no Poinficia Universidad Cat´olicade Chile, Chile [email protected] Kieffer–Pinsker type formulas for Gibbs measures In this talk we will discuss some new results regarding expressions for entropy and pressure in the context of Gibbs measures defined over countable groups. Our starting point will be the
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