EVENT DETAILS AND ABSTRACT

Title: Dynamical Borel-Cantelli Lemmas
Speaker: Professor Dmitry Kleinbock
Speaker Info: Rutgers
Brief Description:
Special Note:
Abstract:

Let $T$ be a measure-preserving transformation of a probability space $X$. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets $A_n\subset X$ and almost every point $x\in X$ the inclusion $T^nx\in A_n$ holds for infinitely many $n$. (A special case $A_1\supset A_2\supset \dots$ gives the "shrinking target" property of the dynamical system.) I will discuss systems which are either symbolic (topological) Markov chains or Anosov diffeomorphisms preserving Gibbs measures, and find sufficient conditions on sequences of cylinders and "rectangles", respectively, that ensure the dynamical Borel-Cantelli lemma. Joint work with Nikolai Chernov.