符号动力系统的因子系统的分布混沌性

广西师范大学学报（自然科学版） ›› 2013, Vol. 31 ›› Issue (4): 66-70.

符号动力系统的因子系统的分布混沌性

康云莲, 刘龙生, 赵俊玲

广西师范大学数学科学学院,广西桂林541004

收稿日期:2013-08-05 出版日期:2013-12-20 发布日期:2018-11-26
通讯作者: 赵俊玲(1975—),女,河南驻马店人,广西师范大学副教授,博士。E-mail:jlzhao@mailbox.gxnu.edu.cn
基金资助:
广西高校科学技术研究项目(2013YB038);国家自然科学基金资助项目(11261008)

Distributional Chaotic Property of the Factor System of Symbolic Dynamical System

KANG Yun-lian, LIU Long-sheng, ZHAO Jun-ling

College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China

Received:2013-08-05 Online:2013-12-20 Published:2018-11-26

摘要/Abstract

摘要： 设(Σ,σ)是两个符号的动力系统,(X,f)是紧致系统,如果存在连续满射h:Σ→X,使得h σ=f h,则称(X,f)是(Σ,σ)的因子系统。本文证明了若(Σ,σ)的因子系统是不可数集,则它是分布混沌的。

关键词: 符号动力系统, 因子系统, 分布混沌

Abstract: Let (Σ,σ) be a dynamical system which has two symbols,and (X,f) be a compact system.If there exists a continuous map h of Σ→X,such that h σ=f h,then (X,f) is the factor system of (Σ,σ).It is proved that if the factor system of (Σ,σ) is uncountable set,then it is distributionally chaotic.

Key words: symbolic dynamical system, factor system, distributional chaos

中图分类号:

康云莲, 刘龙生, 赵俊玲. 符号动力系统的因子系统的分布混沌性[J]. 广西师范大学学报（自然科学版）, 2013, 31(4): 66-70.

KANG Yun-lian, LIU Long-sheng, ZHAO Jun-ling. Distributional Chaotic Property of the Factor System of Symbolic Dynamical System[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(4): 66-70.

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