摘要
通过引进强链遍历性的概念,证明了f拓扑遍历蕴含f强链遍历.对任意正整数k,fk强链遍历蕴含f强链遍历;若f满足Lipschitz条件,k是任意正整数,f强链遍历当且仅当fk强链遍历.集值映射f:κ(X)→κ(X)强链遍历蕴含f:X→X强链遍历.证明了紧致系统(X,f)的强链遍历性与其提升系统(X槇,f槇)的强链遍历性是等价的.
The paper proves that f topologically ergodic implies f strongly chain ergodie by introdu- cing the definition of strongly chain ergodicity. It shows fk strongly chain ergodic implies f strongly chain ergodic for every positive integerk; If f satisfies Lipschitz condition, fk strongly chain ergodic if and only if f strongly chain ergodic for every positive integerk. The paper investigates set-valued map f:κ(X)→κ(X) strongly chain ergodic implies f: X→X strongly chain ergodic, and it also proves that strongly chain ergodic property of (X,f) and strongly chain ergodic property for its lift system (~X,~f) is equivalent.
出处
《武汉大学学报(理学版)》
CAS
CSCD
北大核心
2011年第2期141-144,共4页
Journal of Wuhan 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(2011174)
四平市科技发展计划项目
关键词
强链遍历性
集值映射
提升系统
strongly chain ergodicity
set-valued map
lift systems