拓扑空间中Devaney混沌的乘积性质  

On product property of Devaney chaos maps in topology space

作　　者：索宇[1] 朱培勇[1] 吴新星[1] 

机构地区：[1]电子科技大学数学科学学院,四川成都611731

出　　处：《西南民族大学学报（自然科学版）》2011年第2期199-202,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(10671134)

摘　　要：主要讨论在一般的拓扑空间中Devaney混沌映射的乘积映射是否是混沌的.首先我们研究了判定Devaney混沌的条件,得到周期点是稠密的映射的乘积映射是周期点稠密,但拓扑传递的映射的乘积映射不一定是拓扑传递的.然后给出一个反例说明两个混沌映射的乘积映射不一定是混沌的.最后我们又引入了拓扑混合的概念,由此得到混沌映射的乘积映射是混沌的充分条件.This paper discusses whether the product of chaotic maps （in the sense of Devaney） is chaotic. First it remarks that if maps posse dense periodic points, so does their product. But the product of topologically transitive maps need not be topologically transitive, Then we give a counterexample showing that the product of chaotic maps need not be chaotic. Finally we introduce the concept of topologically mixing and give sufficient conditions under which the product of two chaotic maps is chaotic.

关 键 词：DEVANEY混沌 乘积映射 拓扑混合 拓扑传递 周期轨 

分 类 号：O189[理学—数学]