集值离散动力系统的极限行为

The Limit Behavior of Set-valued Discrete Dynamics

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。

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 Hausdorffmeasurement 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） = lf（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 off, and the inner relation of these limit behavior between （X, f） and （K （X）,f）.