集值离散动力系统的极限行为

设(X,d)为紧致度量空间,f:X→X连续,K(X)是由X的所有非空紧致子集构成的集族,H是由d所诱导的Hausdorff度量,则(K(X),H)是由X的所有非空紧致子集构成的紧致度量空间,-f:K(X)→K(X)连续,-f(A)={f(x):x∈A}研究了-f的扩张性、点态稳定性、性质p、链可迁(混合)、伪轨跟踪性质,以及这些极限行为在(X,f)与(K(X),-f)之间的内在联系。

The Limit Behavior of Set-valued Discrete Dynamics

Make(X,d) a compact metric space,f:X→X is continuous,K(X) is a set consisting of all non-empty compact subsets of X and H is Hausdorff measurement induced by d,so(K(X),H) is a compact metric space consisting of all non-empty compact subsets of X,f:K(X)→K(X) is continuous,f(A)={f(x)|x∈A}.We study the expansion,the stability state of points,the property of p,transitive chain(blended),the properties of false rail track of f,and the inner relation of these limit behavior between(X,f) and(K(X),f).