拓扑熵为log 1.618的符号动力系统  

A Kind of Symbolic Dynamical System with Topological Entropy log 1.618

作　　者：王肖义[1] 李明军[2] 

机构地区：[1]广东商学院华商学院,广州511300 [2]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《数学学报（中文版）》2009年第5期891-896,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10676031);教育部博士点新教师基金资助项目(20070530003)

摘　　要：拟移位映射是符号空间上一类特殊的混沌映射,被广泛关注。本文证明:拟移位映射和移位映射拓扑共轭,从而揭示出拟移位映射是移位映射的一个重要的拓扑共轭系统。同时构造了一类拓扑熵为log1.618的符号动力系统,且该系统是在Devaney意义下混沌的。另外,得到了一类以整个符号空间为极小集的非混沌动力系统。Model shift maps is a class of special chaotic maps on symbolic space and received much attention. In this paper, we proved that on one-sided symbolic space, model shift map is topologically conjugate with the traditional shift map. Also we found a kind of symbolic dynamical system with topological entropy log1.618, and it＇s chaos in the sense of Devaney. At last, we found a special map with the whole symbolic space as its minimal set and which is not chaos.

关 键 词：拟移位映射 帐篷映射 拓扑熵 

分 类 号：O189.1[理学—数学]