混沌群作用  

Chaotic group actions.

作　　者：苏郇立[1] 

机构地区：[1]浙江大学数学系,浙江杭州310027

出　　处：《浙江大学学报（理学版）》2005年第1期13-16,共4页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(10071069).

摘　　要：对紧度量空间X,离散群T,给出了动力系统(X,T)Li-Yorke混沌的定义,并讨论了Devaney混沌和Li-Yorke混沌的关系.指出对可迁系统(X,T),如果作用群T可交换,则对 x∈X,渐近类A(x)是X的第1纲集.并由此证明了当T可交换时,若可迁系统(X,T)包含周期点,则(X,T)是Li-Yorke混沌的.于是当群可交换时Devaney混沌强于Li-Yorke混沌.For compact metric space X and discrete group T, the definition is given of chaos of transformation group (X,T), and the relationship is discussed between the Devaney's chaos and Li-Yorke's chaos.It is proved that for transitive system (X,T), when acting group T is Abelian,the asymptotic class AR(x)is of first category of X for x∈X. Therefore, it is implied that when the acting group is Abelian,the transitive system containing periodic points implies Li-Yorke's chaos, so when acting group is Abelian, Devaney's chaos implies Li-Yorke's chaos.

关 键 词：混沌 初值敏感性 包络半群 邻近 渐近 

分 类 号：O189.1[理学—数学] O192[理学—基础数学]