论文标题
在Lipschitz曲折下复发的动态borel-cantelli引理
Dynamical Borel-Cantelli Lemma for Recurrence under Lipschitz Twists
论文作者
论文摘要
在对某些动力学系统的研究中，一系列可测量集的LIMSUP通常引起了人们的关注。收缩的目标和复发是与LIMSUP集有关的两个最常见的问题。但是，缩小靶标和复发的零法律通常会分别治疗，并以不同的方式进行治疗。在本文中，我们引入了一个广义定义，可以专门研究缩小的目标和复发。我们的方法为这两个问题提供了零一法律的统一证明。
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.
