非紧致度量空间上的持久性  

Persistence on Noncompact Metric Spaces

作　　者：柳佳慧 董美花[1] LIU Jiahui;DONG Meihua(College of Science,Yanbian University,Yanji 133002,Jilin Province,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《吉林大学学报（理学版）》2024年第5期1022-1026,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12201541)。

摘　　要：考虑非紧致度量空间上同胚的持久性问题,利用同胚的持久性、等度连续性、强拓扑稳定性、持久跟踪性等定义,证明:等度连续且拓扑稳定的同胚是持久的;同胚有持久跟踪性当且仅当该同胚是持久的且有伪轨跟踪性;有持久跟踪性的可扩同胚是强拓扑稳定的.We considered the persistence problem of homeomorphism on noncompact metric spaces.By using the definitions of persistence,equicontinuity,strongly topological stability,and persistent shadowing property of homeomorphisms,we prove that homeomorphisms that are equicontinuity and topologically stable are persistent,homeomorphisms have persistent shadowing properties if and only if they are persistent and have pseudoorbital shadowing properties,and an expansive homeomorphis m with persistent shadowing property is strongly topologically stable.

关 键 词：持久性 等度连续性 强拓扑稳定性 持久跟踪性 非紧致度量空间 

分 类 号：O189.11[理学—数学]