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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2021; 58(2): 439-449

Online first article July 28, 2020      Printed March 1, 2021

https://doi.org/10.4134/JKMS.j200095

Copyright © The Korean Mathematical Society.

Topological stability and shadowing property for group actions on metric spaces

Yinong Yang

Beihang University

Abstract

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In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if $G$ is a finitely generated virtually nilpotent group and there exists $g\in G$ such that if $T_g$ is expansive and has the shadowing property, then $T$ is topologically stable.

Keywords: Topological stability, shadowing property, expansiveness, group actions

MSC numbers: 37C85, 37C75, 37C50, 54H20

Supported by: This work was financially supported by China Postdoctoral Science Foundation 2020M670082

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