On multi-transitivity with respect to a vector

被引：20

作者：

Chen ZhiJing ^{[1
]}

Li Jian ^{[2
]}

Lu Jie ^{[3
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

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

[3] S China Normal Univ, Sch Math, Guangzhou 510631, Guangdong, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2014年 / 57卷 / 08期

基金：

中国国家自然科学基金;

关键词：

multi-transitivity; weak mixing; Furstenberg family; Li-Yorke chaos; POINTS;

D O I：

10.1007/s11425-014-4797-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A topological dynamical system (X, f) is said to be multi-transitive if for every n a a"center dot the system (X (n) , f x f (2) x aEuro broken vertical bar x f (n) ) is transitive. We introduce the concept of multi-transitivity with respect to a vector and show that multi-transitivity can be characterized by the hitting time sets of open sets, answering a question proposed by Kwietniak and Oprocha (2012). We also show that multi-transitive systems are Li-Yorke chaotic.

引用

页码：1639 / 1648

页数：10

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