BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:4831@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20230621T093000 DTEND;TZID=Europe/Paris:20230621T173000 DTSTAMP:20240524T072506Z URL:https://www.i2m.univ-amu.fr/evenements/marsavignon23/ SUMMARY: (...): Journée Systèmes Dynamiques Marseille-Avignon 2023 : dyna mique symbolique DESCRIPTION:: Marie-Pierre Béal a dû annuler sa venue.\n\n \n9h45 : Ilkk a Törmä (Université de Turku\, Finlande) : Generic limit sets of cellul ar automata: structure and applications\nA cellular automaton is a dynamic al system consisting of an infinite line of cells\, each of which stores a state that comes from a finite set. The line evolves in discrete time ste ps. On each step\, each cell assumes a new state based on the previous sta tes of itself an some finite set of neighboring cells\, using the same tra nsition rule everywhere.\nOne way to capture the long-term behavior of a d ynamical system is its limit set. The Ω-limit set contains those points o f the phase space with an infinite chain of predecessors. The µ-limit set aims to capture the probable behavior starting from a randomly chosen ini tial conditon\, and the generic limit set contains the limit points of a t opologically large set of initial conditions.\nWe prove various constraint s on the structure of the generic limit set of a cellular automaton\, and in some cases\, present corresponding realization results. We also show ho w the generic limit set can be used to constrain the probable evolution of a cellular automaton model starting from a random initial configuration\, such as a deterministic system of interacting particles.\n \;\n \n11 h15 : Pierre Arnoux (Université d'Aix-Marseille) : Some very much curious dynamical systems coming from number theory\n \;\n \n12h15 : buffet\ n \;\n \n14h00 : Dominik Kwietniak (Université Jagellonne\, Pologne) : An anti-classification theorem for the topological conjugacy problem of Cantor minimal systems\nThe isomorphism problem in dynamics dates back to a question of von Neumann from 1932: Is it possible to classify (in some reasonable sense) the ergodic measure-preserving diffeomorphisms of a comp act manifold up to isomorphism? We would like to study a similar problem: let C be the Cantor set and let Min(C) stand for the space of all minimal homeomorphisms of the Cantor set. Recall that a Cantor set homeomorphism f is in Min(C) if every orbit of f is dense in C. We say that f and g in Mi n(C) are topologically conjugate if there exists a Cantor set homeomorphis m h such that f∘h=h∘g. We prove an anti-classification result showing that even for very liberal interpretations of what a "reasonable'' classif ication scheme might be\, a classification of minimal Cantor set homeomorp hism up to topological conjugacy is impossible. We see it as a consequence of the following: we prove that the topological conjugacy relation of Can tor minimal systems TopConj treated as a subset of Min(C)×Min(C) is compl ete analytic. In particular\, TopConj is a non-Borel subset of Min(C)×Min (C). Roughly speaking\, it means that it is impossible to tell if two mini mal Cantor set homeomorphisms are topologically conjugate using only a cou ntable amount of information and computation.\nOur result is proved by app lying a Foreman-Rudolph-Weiss-type construction used for an anti-classific ation theorem for ergodic automorphisms of the Lebesgue space. We find a c ontinuous map F from the space of all trees over non-negative integers wit h arbitrarily long branches into the class of minimal homeomorphisms of th e Cantor set. Furthermore\, F is a reduction\, which means that a tree T i s ill-founded if and only if F(T) is topologically conjugate to its invers e. Since the set of ill-founded trees is a well-known example of a complet e analytic set\, we see that it is essentially impossible to classify whic h minimal Cantor set homeomorphisms are topologically conjugate to their i nverses.\nThis is joint work with Konrad Deka\, Felipe García-Ramos\, Kos ma Kasprzak\, Philipp Kunde (all from the Jagiellonian University in Krak ów).\n \;\n \n15h30 : soutenance de thèse de Firas Ben Ramdhane (Un iversité d'Aix-Marseille et Université de Sfax\, Tunisie) : Symbolic dyn amical systems in topological spaces defined via edit distances\nIn this t hesis\, we study symbolic dynamical systems on spaces defined from edit di stances\, in particular the spaces of Besicovitch and Weyl. These are metr ic spaces defined using pseudo-metrics and quotients by the relation of ps eudo-metric zero. For this purpose\, we start by studying these two pseudo -metrics which depend on the Hamming distance.\nWe give a generalization o f these two pseudo-metrics (centered and sliding) by replacing the Hamming distance by any distance defined on the set of finite words. Then\, we pr esent some properties of these two pseudo-metrics: measurability\, continu ity\, shift invariance and behavior on periodic configurations. On the oth er hand\, these two pseudo-metrics are defined as an upper limit. For this reason\, we study the existence of the limit for each pseudo-metric.\nWe show that the centered pseudo-metric is not always a limit. Moreover\, we show that in some class of subshifts equipped with the Cantor topology\, t he set where the centered pseudo-metric reaches the maximum and the lower limit is zero is a dense Gδ. Furthermore\, we show that the set where thi s pseudo-metric is a limit is of full measure for any weakly-mixing measur e and that this limit does not depend on the choice of configurations.\nIn contrast\, we show that the sliding pseudo-metric is always a limit. More over\, in some class of subshifts equipped with the Cantor topology\, the set where this pseudo-metric reaches the maximum is a dense Gδ. In additi on\, the set where this pseudo-metric is maximum (within the support of a weakly-mixing measure) is of full measure.\nFinally\, we give a first stud y of dill maps (which generalize cellular automata and substitutions) over the Besicovitch\, Weyl and the Feldman-Katok spaces (the latter is obtain ed by changing the Hamming distance by that of Levenshtein).\nWe prove tha t all dill maps are well-defined over the Feldman-Katok space\, in contras t to the Besicovitch and the Weyl spaces where only uniform and constant d ill maps are well defined. Furthermore\, we show that the Feldman-Katok sp ace is a suitable playground to study the dynamics of dill maps. Indeed\, we prove that the shift is equal to the identity\, there are no expansive cellular automata\, every substitution admits at least one equicontinuous point.\n \;\n CATEGORIES:Séminaire,Journée(s) LOCATION:Saint-Charles - FRUMAM (2ème étage)\, 3 Place Victor Hugo\, Mar seille\, 13003\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM ( 2ème étage):geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20230326T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR