数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1408-1414.doi: 10.1016/S0252-9602(12)60109-X

• 论文 • 上一篇    下一篇

POSITIVE UPPER DENSITY POINTS AND CHAOS

尹建东1*|周作领2   

  1. 1.Department of Mathematics, Nanchang University, Nanchang 330031, China; 2.Lingnan College, Zun Yat-Sen University, Guangzhou 510275, China
  • 收稿日期:2010-11-23 修回日期:2011-08-29 出版日期:2012-07-20 发布日期:2012-07-20
  • 通讯作者: 尹建东, yjdaxf@163.com E-mail:yjdaxf@163.com;lnszzl@mail.sysu.edu.cn
  • 基金资助:

    This work is financially supported by the Foundation(GJJ11295) from the Education Department of Jiangxi.

POSITIVE UPPER DENSITY POINTS AND CHAOS

 YIN Jian-Dong1*, ZHOU Zuo-Ling2   

  1. 1.Department of Mathematics, Nanchang University, Nanchang 330031, China; 2.Lingnan College, Zun Yat-Sen University, Guangzhou 510275, China
  • Received:2010-11-23 Revised:2011-08-29 Online:2012-07-20 Published:2012-07-20
  • Contact: YIN Jian-Dong, yjdaxf@163.com E-mail:yjdaxf@163.com;lnszzl@mail.sysu.edu.cn
  • Supported by:

    This work is financially supported by the Foundation(GJJ11295) from the Education Department of Jiangxi.

摘要:

In this work, we mainly investigate the problem of complexity for a topologi-cally dynamical system (X, f). We prove that f has a full measure center if there exists a countable base {Ui}i=0 of X satisfying that, for any i, there is y in X such that N(y,Ui) is a positive Banach upper density set. Moreover, we consider the chaotic property of (X, f). We show that such a system is chaotic in the sense of Takens-Ruelle if it is transitive but not minimal.

关键词: measure center, E-system, chaos

Abstract:

In this work, we mainly investigate the problem of complexity for a topologi-cally dynamical system (X, f). We prove that f has a full measure center if there exists a countable base {Ui}i=0 of X satisfying that, for any i, there is y in X such that N(y,Ui) is a positive Banach upper density set. Moreover, we consider the chaotic property of (X, f). We show that such a system is chaotic in the sense of Takens-Ruelle if it is transitive but not minimal.

Key words: measure center, E-system, chaos

中图分类号: 

  • 58F10