Zero–one laws for eventually always hitting points in rapidly mixing systems

IF 0.6 3区 数学 Q3 MATHEMATICS
Dmitry Kleinbock, Ioannis Konstantoulas, Florian K. Richter
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引用次数: 0

Abstract

In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes and the Gauß map. For such systems, we present tight conditions on the shrinking rate of the targets so that the set of eventually always hitting points is a null set (or co‑null set respectively).
快速混合系统中最终总是命中点的零一定律
在这项工作中,我们研究了收缩目标系统中最终总是命中的点的集合。这些点的长轨道段最终会在未来的所有时间内击中相应的收缩目标。我们将注意力集中在目标的平移表现出近乎完美的相互独立性的系统上,如伯努利方案和高斯图。对于这类系统,我们提出了目标收缩率的严格条件,这样最终总是命中的点的集合就是一个空集(或分别为共空集)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
9
审稿时长
6.0 months
期刊介绍: Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.
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