按序列分布混沌与拓扑混合  

Distribution Chaos in a Sequence and Topologically Mixing

作　　者：杨润生[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,江苏南京210097

出　　处：《数学学报（中文版）》2002年第4期753-758,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19871041);江苏省自然科学基金资助项目(BK2001108)

摘　　要：本文讨论了按序列分布混沌与拓扑混合的关系,并证明了:若X为至少两点的可分局部紧致度量空间,连续映射f:X→X是拓扑混合的,则对于任一正整数递增序列{mi},存在X的c-稠密Fσ子集D是f按{mi}的某子序列的分布混沌集.In this paper, we discuss the relation between the distribution chaos and the topologically mixing, show that if a continuous map f : X→X is topologically mixing, where X is a separable locally compact metric space containing at least two points, then for any increasing sequence {mi} of positive integers there exists an c-dense Fσ subset D of X is the set of distribution chaos of f in some sub-sequence of {mi}.

关 键 词：分布混沌 拓扑混合 拓扑弱混合 拓扑遍历 

分 类 号：O189.3[理学—数学]