诱导超空间连续流的拓扑传递性  

Topological Transitivity for Induced Hyperspace Flows

作　　者：吴玉虎[1] 计东海[1] 

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080

出　　处：《应用泛函分析学报》2013年第3期243-249,共7页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金天元基金(11226128);国家自然科学基金(11171082)

摘　　要：(X,f)为紧拓扑空间X上的连续流,((?)(X),(?))是由(X,f)诱导的紧超空间(?)(X)上的连续流.研究了(X,f)和((?)(X),(?))拓扑传递性之间的关系.证明了如果(X,f)是拓扑传递的,那么((?)(X),(?))也一定是拓扑传递的,并且举例证明了其逆命题不成立.进一步证明了((?)(X),(?))拓扑传递的当且仅当(X,f)是弱混合的.Let(X,f) be a continuous flow on the compact topological space X.(H(X),f) is the natural extension flow of(X,f) to the compact hyperspace H(X).This paper investigates the relationship between topological transitivity of(X,f) and that of(H(X),f).It is shown that if(H(X),f) is topologically transitive then so is(X,f).We give an example to justify that the converse need not be true.Further,it is proved that(H(X),f) is topologically transitive if and only if(X,f) is weakly mixing.

关 键 词：超空间动力系统 拓扑传递性 弱混合性 连续流 

分 类 号：O177.5[理学—数学] O189.1[理学—基础数学]