Dynamical Borel-Cantelli lemma for recurrence theory

Authors：Hussain, Mumtaz; Li, Bing^*; Simmons, David; Wang, Baowei

Source：Ergodic Theory and Dynamical Systems, 2022, 42(6): 1994-2008.

DOI：10.1017/etds.2021.23

• recurrence
• dynamical Borel-Cantelli lemma
• zero-full law
• exponentially mixing

We study the dynamical Borel-Cantelli lemma for recurrence sets in a measure-preserving dynamical system (X, mu, T) with a compatible metric d. We prove that under some regularity conditions, the mu-measure of the following set @@@ R(psi) = {x is an element of X : d(T-n x, x) R+. The applications of our main theorem include the Gauss map, beta-transformation and homogeneous self-similar sets.

• Institution
  5; 华中科技大学