超空间与原空间动力系统之间的关系  

The relationships between hyperspace dynamical systems and original space

作　　者：李金金[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纯粹数学与应用数学》2014年第1期60-68,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11301417);国家青年基金(11371292)

摘　　要：设(X,d,f)为拓扑动力系统,其中X为局部紧可分的可度量化空间,d为紧型度量,f为完备映射,用2X表示由X的所有非空闭子集构成的集族,(2X,ρ,2f)为由(X,d,f)所诱导的赋予hit-or-miss拓扑的超空间动力系统.本文引入了余紧点传递和弱拓扑传递的定义.特别的,在X满足一定的条件时,给出了点传递,弱拓扑传递和余紧点传递之间的关系,并研究了(X,d,f)的余紧传递点,回复点和几乎周期点分别与(2X,ρ,2f)的传递点,回复点和几乎周期点之间的蕴含关系.这些结论丰富了赋予hit-or-miss拓扑的超空间的研究内容.Let （X, d, f ） be a topological dynamical system, where X is a locally compact separable metrizable space, d is a compact-type metric and f is a perfect mapping. Let 2X be the space of all non-empty closed subsets of X. Let （2X,ρ,2f） denote the hyperspace dynamical systems induced by （X,d,f） equipped with the hit-or-miss topology. In this paper, the concepts of co-compact point transitivity and weak topological transitivity are introduced. In particular, when X satisfies certain condition, the relationships between point transitivity, weak topological transitivity and co-compact point transitivity are given, and the author studied the relationships between co-compact transitivity point, recurrent point and almost period point of （X, d, f ） respectively and transitivity point, recurrent point and almost period point of （2X ,ρ, 2f ）. These conclusions enriched the contents of induced hyperspace dynamical systems equipped with the hit-or-miss topology.

关 键 词：超空间动力系统 弱拓扑传递 余紧点传递 回复点 几乎周期点 

分 类 号：O189.11[理学—数学]