Noticias en español
On the relation between topological entropy and asymptotic pairs.
ABSTRACT: I will present some results that state that under certain topological conditions, any action of a countable amenable group with positive topological entropy admits off-diagonal asymptotic pairs. I shall explain the latest results on this topic and present a new approach, inspired from thermodynamical formalism and developed in collaboration with Felipe García-Ramos and Hanfeng Li, which unifies all previous results and yields new classes of algebraic actions for which positive entropy yields non-triviality of their associated homoclinic group.
Read MoreDistorted diffeomorphisms and regularity.
ABSTRACT: The goal is to deal with the following question: for a compact manifold M, does there exist a diffeomorphism that is distorted in the group of C^r diffeomorphisms yet undistorted in the group of C^s diffeomorphism, where 1 \leq r < s ? Although the answer seems to be positive, it seems hard to build explicit examples (these diffeomorphisms necessarily have zero entropy). We will provide such examples for the closed unit interval for r = 1 and s = 2. The distortion part of the proof uses standard techniques on centralizers; the C^2 part uses recent work with Hélène Eynard on the...
Read MoreSuspension flows over countable Markov shifts.
ABSTRACT: Markov shifts have been systematically used to model discrete time dynamical systems with certain hyperbolicity. In the same spirit suspension flows over Markov shifts model some continuous time systems (e.g. uniformly hyperbolic flows on compact manifolds), where the flow has a transverse section with specified return time. In this talk I will discuss the entropy theory of the suspension flow over a countable Markov shift (a Markov shift with countable alphabet). I will focus on the entropy at infinity of the flow (a natural quantity in the non-compact case) and compactness of the...
Read MorePredictive sets
ABSTRACT: A subset of the integers P is called predictive if for all zero-entropy processes X_i; i in Z, X_0 can be determined by X_i; i in P. The classical formula for entropy shows that the set of natural numbers forms a predictive set. In joint work with Benjamin Weiss, we will explore some necessary and some sufficient conditions for a set to be predictive. These sets are related to Riesz sets (as defined by Y. Meyer) which arise in the study of singular measures. This and several questions will be discussed during the talk. No previous background will be assumed on the subject.
Read MoreDynamics of unipotent frame flows on hyperbolic manifolds.
ABSTRACT: Joint work with B. Schapira. After explaining the geometry of the objects, we give another proof of a theorem of A. Mohammadi and H. Oh about the ergodicity of the Burger-Roblin measure for Kleinian groups of high enough critical exponents, and relate it with a topological counterpart.
Read MoreDynamics of unipotent frame flows on hyperbolic manifolds
ABSTRACT: Joint work with B. Schapira. After explaining the geometry of the objects, we give another proof of a theorem of A. Mohammadi and H. Oh about the ergodicity of the Burger-Roblin measure for Kleinian groups of high enough critical exponents and relate it with a topological counterpart.
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