Topological Stability and Pseudo-orbit Tracing Property for Homeomorphisms on Uniform Spaces

被引：0
作者：
Ke Song Yan
Fan Ping Zeng
机构：
[1] Guangxi University of Finance and Economics,School of Information and Statistics
来源：
Acta Mathematica Sinica, English Series | 2022年 / 38卷
关键词：
Topological stability; pseudo-orbit tracing property; expansiveness; uniform space; 37C50; 37C75; 54E15; 54H20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces. We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property, then it is topologically stable. Moreover, we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization. We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.
引用
收藏
页码：431 / 442
页数：11
相关论文
共 50 条
[1]  
Ahmadi S A(2017)Shadowing, ergodic shadowing and uniform spaces Filomat 31 5117-5124
[2]  
Ahmadi S A(2018)On the entropy points and shadowing in uniform spaces Int. J. Bifurcation and Chaos 28 1850155-100
[3]  
Wu X(2018)Devaney’s and Li—Yorke’s chaos in uniform spaces J. Dyn. Control Syst. 24 93-3544
[4]  
Feng Z(2017)Topological stability from Gromov—Hausdorff viewpoint Discrete Contin. Dyn. Syst. 37 3531-339
[5]  
Arai T(1975)-limit sets for Axiom A diffeomorphism J. Differential Equations 18 333-1167
[6]  
Arbieto A(1960)On expansive homeomorphisms Pacific J. Math. 10 1163-357
[7]  
Morales C A(2013)Sensitivity and Devaney’s chaos in uniform spaces J. Dyn. Control Syst. 19 349-1057
[8]  
Bowen R(2018)Topological stability and pseudo-orbit tracing property of group actions Proc. Amer. Math. Soc. 146 1047-267
[9]  
Bryant B F(2018)Various types of shadowing and specification on uniform spaces J. Dyn. Control Syst. 24 253-1942
[10]  
Ceccherini-Siberstein T(2012)New and old facts about entropy in uniform spaces and topological groups Topology Appl. 159 1916-641
12345