关于集值离散系统的扩散性  

On scattering property of set-valued discrete systems

作　　者：盛业青[1] 顾荣宝[1] 

机构地区：[1]安徽大学数学与计算科学学院,安徽合肥230039

出　　处：《安徽大学学报（自然科学版）》2005年第3期1-4,共4页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10361001)

摘　　要：设(X,d)为度量空间,f:X→X为连续映射,К(X)是X的所有非空紧致子集组成的集族,H是由d诱导的К(X)上的度量,f:К(X)→К(X)定义为f(K)={f(a):a∈K}.本文讨论了f与f的扩散性之间的关系,证明了当f为同胚时,f的扩散性蕴含f的扩散性,并且在К(X)取We拓扑时,二者相互蕴含.Let (X,d) be a metric space and f:X→X be a continuous map,К(X) be the class of all nonempty compact subsets of X with the Hausdorff metric H induced by d,define f:К(X)→К(X) as f(K)=｛f(a):a∈K｝. In this note,we investigate the relationships between the scattering property of some set-valued discrete dynamical systems associated to f (collective chaos) and the scattering property of f (individual chaos), show that if f is a homeomorphism,f is scattering implies f is scattering in general and f is scattering if and only if f is scattering when К(X) is endowed with the topology of We.

关 键 词：扩散性 离散系统 集值 度量空间 连续映射 紧致子集 集族 同胚 拓扑 

分 类 号：O177[理学—数学] TU528.571[理学—基础数学]