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arXiv · 2205.12366

Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists

Dmitry Kleinbock·Jiajie Zheng
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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.

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Dmitry Kleinbock, Jiajie Zheng. 2022-05-24. Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists. https://doi.org/10.1088/1361-6544/acafcb

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