Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists
- Resource Type
- Working Paper
- Authors
- Kleinbock, Dmitry; Zheng, Jiajie
- Source
- Subject
- Mathematics - Dynamical Systems
Mathematics - Number Theory
37B20, 37D20, 37E05
- Language
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.
Comment: 30 pages; the main theorem of the previous version is slightly weakened, several new theorems added