Dynamical Borel–Cantelli lemma for recurrence under Lipschitz twists
Dynamical Borel–Cantelli lemma for recurrence under Lipschitz twists
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DOI：
10.1088/1361-6544/acafcb
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发表时间：
2022-05
期刊：
影响因子：
1.7
通讯作者：
D. Kleinbock;Jiajie Zheng
中科院分区：
文献类型：
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作者：
D. Kleinbock;Jiajie Zheng
在某些动力系统的研究中，可测集序列的limsup集往往是人们感兴趣的。收缩目标和递归性是limsup集研究中最常见的两个问题。然而，收缩目标和递归的0 - 1定律通常被分开处理并被不同地证明。在本文中，我们引入了一个广义的定义，可以专门到收缩目标和递归，我们的方法给出了一个统一的证明的零-一法律的两个问题。
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.