Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists
Dynamical Systems
2023-02-08 v2 Number Theory
Abstract
In the study of some dynamical systems the limsup set of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limsup sets. However, the zero-one laws for the shrinking targets and recurrence are usually treated separately and proved differently. In this paper, we introduce a generalized definition that can specialize into the shrinking targets and recurrence; our approach gives a unified proof of the zero-one laws for the two problems.
Cite
@article{arxiv.2205.12366,
title = {Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists},
author = {Dmitry Kleinbock and Jiajie Zheng},
journal= {arXiv preprint arXiv:2205.12366},
year = {2023}
}
Comments
30 pages; the main theorem of the previous version is slightly weakened, several new theorems added