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UID:7942@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151215T100000
DTEND;TZID=Europe/Paris:20151215T150000
DTSTAMP:20241120T205610Z
URL:https://www.i2m.univ-amu.fr/evenements/journee-douverture-du-projet-pr
 obabilites-approximations-diophantiennes/
SUMMARY:Journée (I2M\, Luminy\, Marseille): Ouverture du Projet "Probabili
 tés & Approximations Diophantiennes"
DESCRIPTION:Journée: JOURNÉE THÉMATIQUE\nIntervenants :\n-\n- 10h : Paul
 o Varandas (UFBA\, Brazil)\n\n* On the complexity and variational relation
  for semigroup actions\nOne of the main purposes of dynamical systems is t
 o understand the behavior of the space of orbits of continuous group and s
 emigroup actions on compact metric spaces. The most studied and well under
 stood classes of such dynamical systems are ℤ-\, ℕ- or ℝ-actions\, w
 hich correspond to the dynamics of homeomorphisms\, continuous endomorphis
 ms or continuous flows\, respectively. A notion of topological complexity 
 for such dynamical systems has been proposed in the seventies and was very
  well studied by Goodwin\, Bowen\, Walters and Parry\, among others\, and 
 proved a variational principle for the pressure.\nSuch strong relations be
 tween the topological and ergodic features of a dynamical system is still 
 unavailable for general group actions. On the one hand\, the theory is not
  unified since several notions of topological complexity have been propose
 d\, and many of them depend on properties of the group action as commutati
 vity or amenability. On the other hand\, many group actions admit no commo
 n invariant measures and this notion should be replaced by a more flexible
  concept.\nIn this talk I will discuss a notion of topological entropy and
  pressure for finitely generated semigroup actions and discuss its regular
 ity\, relation with the exponential growth of periodic orbits\, properties
  of the ζ function and relation with random dynamical systems in the sett
 ing of finitely generated semigroups of expanding maps.\nThese results are
  part of joint works with F. Rodrigues (UFRGS\, Brazil) and M. Carvalho (U
 . Porto\, Portugal).\n-\n- 11h : Alba Málaga-Sabogal (I2M\, Marseille)\n*
  Mélange générique dans des billards polygonaux et plus...\nConsidéron
 s des polygones dont les côtés sont parallèles à deux vecteurs fixés.
  Gutkin et Katok ont montré que pour toute direction fixée θ il existe 
 un ensemble Gδ dense de polygones pour lesquels le billard est faiblement
  mélangeant en direction θ. Dans cet exposé\, je vais présenter une g
 énéralisation de leur argument qui permet d'obtenir le mélange faible d
 ans un ensemble Gδ-dense de mesure totale de directions pour un polygone 
 générique. Je conclurai alors par une application à la multiple ergodic
 ité du modèle du vent à arbre (Wind-Tree).\nC'est un travail en collabo
 ration avec Serge Troubetzkoy.\n-\n- 14h : Henk Bruin (University of Vienn
 a\, Austria)\n* Matching interval maps\nA somewhat curious phenomenon\, ob
 served in e.g. the family of α-continued fraction maps\, is that certain 
 orbits will synchronize (called matching)\, and lead to a better form of i
 nvariant density and monotonicity properties of entropy than might a prior
 i be expected. The same phenomenon occurs for families of piecewise linear
  interval maps\, but especially the parameter space becomes very interesti
 ng\, and I will present results on this\, which are joint work with Carlo 
 Carminati\, Alessandro Profeti and Stefano Marmi (University of Pisa).\n-\
 nOrganisateur : Serge Troubetzkoy\n
CATEGORIES:Séminaire,Ernest,Journée(s),Manifestation scientifique
LOCATION:I2M Luminy - TPR2\, Amphithéâtre Herbrand 130-134 (1er étage)\,
  163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Amph
 ithéâtre Herbrand 130-134 (1er étage):geo:0,0
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DTSTART:20151025T020000
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