一种新的拓扑熵：余紧拓扑熵  

A new entropy：The entropy of co-compact open cover

作　　者：魏征[1] 王延庚[1] 卫国 

机构地区：[1]西北大学数学系,陕西西安710127 [2]北卡莱罗纳州大学彭布罗克分校数学与计算机科学系,美国北卡莱罗纳州28372

出　　处：《西北大学学报（自然科学网络版）》2009年第1期1-13,共13页

基　　金：陕西省自然科学基金资助项目（SJ08A24）

摘　　要：对一般的Hausdorff拓扑空间上的完备映射定义了余紧拓扑熵。余紧拓扑熵是Alder意义下熵的推广，但又不同于Bowen意义下的熵，它是不同度量下所有Bowen意义下熵的下界。此外，把Lebesgue数定理从紧度量空间上的开覆盖推广到任意度量空间上的余紧开覆盖。Adler,Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces ,but Bowen＇s entropy is metric-dependent .We propose a new definition of topological entropy for prefect mappings on arbitrary Hausdorff topological spaces（compactness, metrizability not necessarily required）,investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and MeAndrew and is metric-independent for metrizable spaces .Yet it holds various basic properties of Adler, Konheim and McAndrew＇s entropy ,e.g. ,the entropy of a subsystem is bounded by that of the original system ,topologically conjugated systems have a same entropy.

关 键 词：拓扑熵 完备映射 余紧开集 余紧开覆盖 LEBESGUE常数 拓扑共轭 

分 类 号：O189.1[理学—数学]