拓扑强链遍历映射

拓扑强链遍历映射 Topological Strongly Chain Ergodicity Maps 孟鑫 MENG Xin 1 first-author 范钦杰 FAN Qinjie 1 王宏仁 WANG Hongren 1 吉林师范大学数学学院 吉林师范大学数学学院 Department of Mathematics,Jilin Normal University Department of Mathematics,Jilin Normal University 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 ergodic by introducing 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. 强链遍历性 集值映射 提升系统 strongly chain ergodicity set-valued map lift systems 10.14188/j.1671-8836.2011.02.017 O189.11 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 2011-02-01 2021-04-01 2 57