一个关于P-混沌蕴涵分布混沌以及具有正拓扑熵的Devaney混沌的注记

数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 269-273.

一个关于P-混沌蕴涵分布混沌以及具有正拓扑熵的Devaney混沌的注记

Department of Mathematics, Nanchang University

收稿日期:2011-11-04 出版日期:2013-06-30 发布日期:2023-03-03
作者简介:YIN Jian-dong(1975-), male, native of Ji'an, Jiangxi, an associate professor of Nanchang University, engages in topological dynamics.
基金资助:
Supported by the Foundation of the Jiangxi Education Department(GJJ11295)； Supported by the Natural Science Foundation of Jiangxi Province(20114BAB201006)

A Note on P-chaos Implies Distributional Chaos and Chaos in the Sense of Devaney with Positive Topological Entropy

Department of Mathematics, Nanchang University

Received:2011-11-04 Online:2013-06-30 Published:2023-03-03
About author:YIN Jian-dong(1975-), male, native of Ji'an, Jiangxi, an associate professor of Nanchang University, engages in topological dynamics.
Supported by:
Supported by the Foundation of the Jiangxi Education Department(GJJ11295)； Supported by the Natural Science Foundation of Jiangxi Province(20114BAB201006)

摘要/Abstract

摘要：

In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.

关键词: P-chaos, pseudo orbit- tracing property, topologically mixing, sub-shift of finite type

Abstract: In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.

Key words: P-chaos, pseudo orbit- tracing property, topologically mixing, sub-shift of finite type

中图分类号:

O189.3

尹建东, 邱玉芬. 一个关于P-混沌蕴涵分布混沌以及具有正拓扑熵的Devaney混沌的注记[J]. 数学季刊, 2013, 28(2): 269-273.

YIN Jian-dong, QIU Yu-fen. A Note on P-chaos Implies Distributional Chaos and Chaos in the Sense of Devaney with Positive Topological Entropy[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 269-273.