Multi-recurrence and van der Waerden systems

被引：12

作者：

Kwietniak, Dominik ^{[1
]}

Li Jian ^{[2
]}

Oprocha, Piotr ^{[3
,4
]}

Ye XiangDong ^{[5
]}

机构：

[1] Jagiellonian Univ Krakow, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[2] Shantou Univ, Dept Math, Shantou 515063, Peoples R China

[3] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

[4] Univ Ostrava, Natl Supercomputing Ctr IT4Innovat, Div Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Ostrava 70103, Czech Republic

[5] Univ Sci & Technol China, Chinese Acad Sci, Sch Math Sci, Wu Wen Tsun Key Lab Math, Hefei 230026, Peoples R China

来源：

SCIENCE CHINA-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; TOPOLOGICAL DYNAMICS; SETS; ENTROPY; THEOREM; SZEMEREDI; RIGIDITY; POINTS;

D O I：

10.1007/s11425-015-0860-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：59 / 82

页数：24

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