集值离散动力系统的拓扑遍历性与链遍历性

广西师范大学学报（自然科学版） ›› 2011, Vol. 29 ›› Issue (1): 20-23.

集值离散动力系统的拓扑遍历性与链遍历性

孟鑫, 范钦杰, 王宏仁

吉林师范大学数学学院,吉林四平136000

收稿日期:2010-10-13 发布日期:2018-11-16
通讯作者: 范钦杰(1956—),女,吉林梅河口人,吉林师范大学教授,博士。E-mail: fanqinjie@sina.com
基金资助:
国家自然科学基金资助项目(10971084);吉林省教育厅“十二五”科学技术研究项目;四平市科技发展计划项目

Topological Ergodicity and Chain Ergodicity of the Set-valuedDiscrete Dynamical Systems

MENG Xin, FAN Qin-jie, WANG Hong-ren

College of Jilin Normal University,Siping Jilin 136000,China

Received:2010-10-13 Published:2018-11-16

摘要/Abstract

摘要： 设f:X→X,f是由f所诱导的集值映射,本文证明了f拓扑遍历蕴涵f拓扑遍历,反之不成立,而在W^e-拓扑下f的拓扑遍历性与f拓扑遍历性等价,继而证明f拓扑遍历与f_m拓扑遍历是等价的;对于某个正整数k,f^k链遍历蕴涵f链历,给出了f在满足POTP前提下,f链遍历的7个等价条件。

关键词: 集值映射, 拓扑遍历, 链遍历

Abstract: Let f:X→X and f be the set-valued mapwhich is induced by f .In the paper,it is proved that if f is topologically ergodic,it implies f is also topologically ergodic,the converse is not true,and the topological ergodicity of f and f is equilant under W^e-topology,then f is topologically ergodic if and only if f_mis topologically ergodic.It is also proved that,for some integerk,if f^k is chain ergodic,it implies f is also chain ergodic.Let f have POTP,7 equilant condtions on f which is chain ergodic are given.

Key words: set-valued maps, topological ergodicity, chain ergodicity

中图分类号:

O189.1

孟鑫, 范钦杰, 王宏仁. 集值离散动力系统的拓扑遍历性与链遍历性[J]. 广西师范大学学报（自然科学版）, 2011, 29(1): 20-23.

MENG Xin, FAN Qin-jie, WANG Hong-ren. Topological Ergodicity and Chain Ergodicity of the Set-valuedDiscrete Dynamical Systems[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 20-23.

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