Multi-recurrence and van der Waerden systems
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- 作者：Dominik Kwietniak ; Jian Li ; Piotr Oprocha ; XiangDong Ye
- 关键词：multi ; recurrent points ; van der Waerden systems ; multiple recurrence theorem ; multiple IP ; recurrence property ; multi ; non ; wandering points
- 刊名：Science China Mathematics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：60
- 期：1
- 页码：59-82
- 全文大小：381KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Applications of Mathematics;
- 出版者：Science China Press
- ISSN：1869-1862
- 卷排序：60
文摘
We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.