# Séminaires : Séminaire de Systèmes Dynamiques

 Equipe(s) : gd, Responsables : H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez Email des responsables : Salle : 15-25-502 Adresse : Campus Pierre et Marie Curie Description Archive avant 2015 Hébergé par le projet Géométrie et Dynamique de l’IMJ

 Orateur(s) Philipp Kunde - Hambourg, Titre Dichotomy results for eventually always hitting time statistics Date 15/10/2021 Horaire 14:00 à 15:45 Diffusion Résume The term \emph{shrinking target problems} in dynamical systems describes a class of questions which seek to understand the recurrence behavior of typical orbits of a dynamical system. The standard ingredients of such questions are a probability measure preserving dynamical system $(X,\mu, T)$ and a sequence of targets $\{B_m\}_{m\in \mathbb{N}}$ with $B_m\subset X$ and $\mu(B_m)\to 0$. Classical questions in this area focus on the set of points whose $n$-th iterate under $T$ lies in the $n$-th target for infinitely many $n$. We study a uniform analogue of these questions, the so-called \emph{eventually always hitting points}. These are the points whose first $n$ iterates will never have empty intersection with the $n$-th target for sufficiently large $n$. I will talk about necessary and sufficient conditions on the shrinking rate of the targets for the set of eventually always hitting points to be of full or zero measure. In particular, I will present some recent dichotomy results for some interval maps obtained in collaboration with Mark Holland, Maxim Kirsebom, and Tomas Persson. Salle 15-25-502 Adresse Campus Pierre et Marie Curie