ω混沌与伪移位不变集  

ω-Chaos and Pseudo-Shift Invariant Set

作　　者：姜海景[1] 宋琛[2] 

机构地区：[1]南京航空航天大学理学院南京,210016 [2]无锡市广播电视大学无锡,214021

出　　处：《南京航空航天大学学报》2000年第5期551-555,共5页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：就紧致度量空间的连续自映射 ,研究了具有半伪移位不变集与 ω混沌的关系。证明了若 f有半伪移位不变集 ,则 f是ω混沌的且存在不可数集 S R(f ) - R(f ) ,其中 S既为 f的ω紊乱集又为 f的 L i- Yorke意义下的混沌集。进而导出一维映射 f拓扑熵大于零的充要条件是存在正整数 n,使得 fnω混沌且存在 fn 的不可数的 ω紊乱集 S R(f) - R(f)Let (X,d) be a compact metrizable space and f:X→X be continuous. This paper denotes that by R(f) the set of recurrent points and R(f) the closure of R(f) and studies the relations between that f has the semi pseudo shift invariant set and that f is ω chaos. We proved that if f has the semi pseudo shift invariant set, then f is ω chaos and there is an uncountable ω scrambled set S R(f) -R(f) , here S is also the chaotic set in the sense of Li Yorke. Furthermore, the topological entropy of one dimensional map f is proved to be positive if and only if there is n∈N such that f n is ω chaotic and there exists an uncountable ω scrambled set S R(f) -R(f) .

关 键 词：拓扑熵 混沌 一维映射 ω混沌 伪移位不变集 

分 类 号：O177.3[理学—数学] O189.11[理学—基础数学]