Multi-recurrence and van der Waerden systems

被引：0
|
作者：
KWIETNIAK Dominik [1 ]
LI Jian [2 ]
OPROCHA Piotr [3 ,4 ]
YE XiangDong [5 ]
机构：
[1] Faculty of Mathematics and Computer Science, Jagiellonian University in Kraków
[2] Department of Mathematics, Shantou University
[3] Faculty of Applied Mathematics, AGH University of Science and Technology
[4] National Supercomputing Centre IT4Innovations, Division of the University of Ostrava,Institute for Research and Applications of Fuzzy Modeling, University of Ostrava
[5] Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences,School of Mathematical Sciences, University of Science and Technology of China
来源：
ScienceChina(Mathematics) | 2017年 / 60卷 / 01期
基金：
中国国家自然科学基金;
关键词：
multi-recurrent points; van der Waerden systems; multiple recurrence theorem; multiple IP-recurrence property; multi-non-wandering points;
D O I：
暂无
中图分类号：
O19 [动力系统理论];
学科分类号：
070104 ; 0711 ; 071101 ;
摘要：
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.
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页码：59 / 82
页数：24
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