{"title":"Topological stability and pseudo-orbit tracing property of Borel measures from the viewpoint of open covers","authors":"Shuzhen Hua, Jiandong Yin","doi":"10.1080/14689367.2023.2226384","DOIUrl":null,"url":null,"abstract":"In the paper, we introduce the concepts of topological stability, expansivity and pseudo-orbit tracing property of Borel measures with respect to a given continuous map on a compact topological space from the viewpoint of open covers and prove that every expansive Borel measure with the pseudo-orbit tracing property is topologically stable. Furthermore, we obtain some properties of topologically stable measures.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"597 - 611"},"PeriodicalIF":0.5000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2023.2226384","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In the paper, we introduce the concepts of topological stability, expansivity and pseudo-orbit tracing property of Borel measures with respect to a given continuous map on a compact topological space from the viewpoint of open covers and prove that every expansive Borel measure with the pseudo-orbit tracing property is topologically stable. Furthermore, we obtain some properties of topologically stable measures.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
