混沌集的基数  

Cardinalities of Scrambled Sets

作　　者：周雷[1] 

机构地区：[1]上海工程技术大学基础教学学院,上海201620

出　　处：《上海工程技术大学学报》2006年第3期235-239,共5页Journal of Shanghai University of Engineering Science

摘　　要：在数学中,有许多关于混沌函数、混沌集及其基数结果。为此证明了对于任意基数α≥|R|,存在度量空间X上的连续映射f,使得f有一个基数为α的混沌集,但没有基数为β(>α)的混沌集。而后通过构造右移同胚的方式,证明了存在连通的紧致度量空间(X,d)及其上面的连续映射f:X→X,使得f有一个不可数混沌集但没有可数无限的c混沌集,其中c为任意正实数。Chaotic phenomena have attracted a great deal of attention in recent years. There are many results about chaotic functions and scrambled sets in the mathematics field. For any cardinality α≥｜R｜ , where ｜ R ｜ denotes the cardinality of the real numbers, there exists a continuous map f from a metric space X to itself which has a scrambled set with cardinality a but has no scrambled set with greater cardinality. Then, it was shown that there exist compactly connected metric space （X, d ） and a continuous map f from X itself, so that f has a uncountable scrambled set but has no countable infinite positively scrambled set.

关 键 词：动力系统 混沌集 迁移映射 右移同胚 基数 

分 类 号：O19[理学—数学] O189.11[理学—基础数学]