集值离散动力系统的拓扑遍历性与链遍历性  

Topological Ergodicity and Chain Ergodicity of the Set-valued Discrete Dynamical Systems

作　　者：孟鑫[1] 范钦杰[1] 王宏仁[1] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《广西师范大学学报（自然科学版）》2011年第1期20-23,共4页Journal of Guangxi Normal University:Natural Science Edition

基　　金：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

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We-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fm拓扑遍历是等价的;对于某个正整数k,fk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。Let f：X→X and f-be the set-valued map which 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 Wetopology,then f-is topologically ergodic if and only if f-m is topologically ergodic.It is also proved that,for some integer k,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.

关 键 词：集值映射 拓扑遍历 链遍历 

分 类 号：O189.1[理学—数学]