| 拓扑强链遍历映射 |
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| 引用本文： | 孟鑫,范钦杰,王宏仁.拓扑强链遍历映射[J].武汉大学学报(理学版),2011,57(2):141-144. |
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| 作者姓名： | 孟鑫 范钦杰 王宏仁 |
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| 作者单位： | 吉林师范大学数学学院,吉林,四平,136000 |
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| 基金项目： | 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 |
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| 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.
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| 关 键 词： | 强链遍历性 集值映射 提升系统 |
Topological Strongly Chain Ergodicity Maps |
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| MENG Xin,FAN Qinjie,WANG Hongren.Topological Strongly Chain Ergodicity Maps[J].JOurnal of Wuhan University:Natural Science Edition,2011,57(2):141-144. |
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| Authors: | MENG Xin FAN Qinjie WANG Hongren |
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| Affiliation: | MENG Xin,FAN Qinjie,WANG Hongren(Department of Mathematics,Jilin Normal University,Siping 136000,Jilin,China) |
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| Abstract: | 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. |
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| Keywords: | strongly chain ergodicity set-valued map lift systems |
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