Théorie Ergodique à Paris 13
Université Paris 13, Villetaneuse, 15-17 septembre, 2008Résumés
Jon Aaronson
(Tel-Aviv University)
Limit properties of infinite transformations and their return time stochastic processes. This will be a review of some distributional and pointwise limit properties of some infinite transformations (and hence their return time stochastic processes) and - some new applications of the Darling-Kac method to ''weakly pointwise dual ergodic'' transformations yielding eg the stable limit theorems and (other) law of the iterated logarithm for certain positive statiionary processes (work in progress with Roland Zweimuller); -- a distributional limit theorem for transformations like the Hajian-Ito-Kakutani transformation (work in progress with Omri Sarig).
Limit properties of infinite transformations and their return time stochastic processes. This will be a review of some distributional and pointwise limit properties of some infinite transformations (and hence their return time stochastic processes) and - some new applications of the Darling-Kac method to ''weakly pointwise dual ergodic'' transformations yielding eg the stable limit theorems and (other) law of the iterated logarithm for certain positive statiionary processes (work in progress with Roland Zweimuller); -- a distributional limit theorem for transformations like the Hajian-Ito-Kakutani transformation (work in progress with Omri Sarig).
Oleg Ageev (Moscow
State Technical University)
Typical homeomorphisms of Cantor sets; spectral invariants and embeddings into group actions.
Typical homeomorphisms of Cantor sets; spectral invariants and embeddings into group actions.
Pierre Arnoux
(Institut de Mathématiques de Luminy)
Tilings and endomorphisms of free groups. We will give an overview of some recent progresses on self-similar tilings related to substitutions and endomorphisms of free groups, and on related dynamical systems.
Tilings and endomorphisms of free groups. We will give an overview of some recent progresses on self-similar tilings related to substitutions and endomorphisms of free groups, and on related dynamical systems.
Julien
Brémont
(Université Paris 12)
Random walk in quasi-periodic random environment We consider a one-dimensional random walk with finite range in a random environment defined by an ergodic translation on a torus. For regular data and under a Diophantine condition on the translation, we prove an invariance principle with deterministic centering.
Random walk in quasi-periodic random environment We consider a one-dimensional random walk with finite range in a random environment defined by an ergodic translation on a torus. For regular data and under a Diophantine condition on the translation, we prove an invariance principle with deterministic centering.
Jean-Pierre Conze
(Université de Rennes)
Examples of stationary walks over rotations: recurrence, regularity. We will give different examples of noncompact recurrent extensions of rotations. In particular, we discuss recurrence/transience for extensions of bi-dimensional rotations (joint work with Nicolas Chevallier)
Examples of stationary walks over rotations: recurrence, regularity. We will give different examples of noncompact recurrent extensions of rotations. In particular, we discuss recurrence/transience for extensions of bi-dimensional rotations (joint work with Nicolas Chevallier)
Sylvain Crovisier
(Université Paris 13)
Realization of minimal and uniquely ergodic homeomorphisms on manifolds. In a joint work with F. Beguin and F. Le Roux, we prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses realization techniques by Rees and the following improvement of Weiss relative version of Jewett-Krieger theorem: any extension between two ergodic systems is isomorphic to a skew-product on Cantor sets.
Realization of minimal and uniquely ergodic homeomorphisms on manifolds. In a joint work with F. Beguin and F. Le Roux, we prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses realization techniques by Rees and the following improvement of Weiss relative version of Jewett-Krieger theorem: any extension between two ergodic systems is isomorphic to a skew-product on Cantor sets.
Fabien Durand
(Université de Picardie)
Eigenvalues of finite topological rank Cantor dynamical systems.
Eigenvalues of finite topological rank Cantor dynamical systems.
Krzysztof Frączek
(University of Toruń)
Growth and mixing My talk will be based on a joint paper with Leonid Polterovich. Given a bi-Lipschitz measure-preserving homeomorphism of a compact metric space (with a probability Borel measure) of finite dimension, consider the sequence formed by the Lipschitz norms of its iterations. I shall discuss the growth of this sequence for some classes of homeomorphisms. For homeomorphisms which mix Lipschitz functions I shall present some universal lower estimations on the growth and some lower bounds which depend on the rate of mixing.
Growth and mixing My talk will be based on a joint paper with Leonid Polterovich. Given a bi-Lipschitz measure-preserving homeomorphism of a compact metric space (with a probability Borel measure) of finite dimension, consider the sequence formed by the Lipschitz norms of its iterations. I shall discuss the growth of this sequence for some classes of homeomorphisms. For homeomorphisms which mix Lipschitz functions I shall present some universal lower estimations on the growth and some lower bounds which depend on the rate of mixing.