集值离散动力系统的拓扑遍历性、拓扑熵与混沌  

Topological Ergodicity,Entropy and Chaos of Set-valued Discrete Systems

作　　者：王辉[1] 范钦杰[1] 

机构地区：[1]吉林师范大学数学学院,吉林省四平136000

出　　处：《吉林大学学报（理学版）》2007年第6期903-906,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10271023)

摘　　要：设(X,d)为紧致度量空间,f:X→X连续,(K(X),H)是X所有非空紧致子集构成的紧致度量空间,-f:K(X)→K(X),-f(A)={f(x)x∈A}.通过研究点运动与点集运动的关系,证明了集值映射-f拓扑遍历与f拓扑双重遍历等价并构造一个零拓扑熵且不具有任何混沌性质的紧致系统,其诱导的集值映射-f有无穷拓扑熵且分布混沌,表明集值离散动力系统的拓扑复杂性可以远远大于原系统.Let （X,d） be a compact metric space, f： X→X a continuous map, and （K（X） ,H） a compact metric space consisting of all non-empty compact subsets of X, f： K（X）→K（X）, f（A） = {f（x） ｜x ∈ A } . It has been proved that the topological ergodicity of set-valued map f is equivalent to the topological double ergodicity of f by studying the relation between the motion of points and the motion of sets; moreover, a compact system has been constructed which has zero topological entropy and no chaotic property, but the induced set-valued map of which has infinite topological entropy and distributional chaos, this implies that the topological complexity of f could be far greater than that off.

关 键 词：集值映射 拓扑遍历 拓扑熵 分布混沌 

分 类 号：O189[理学—数学]