Topological stability and shadowing property for group actions on metric spaces
J. Korean Math. Soc. 2021 Vol. 58, No. 2, 439-449
https://doi.org/10.4134/JKMS.j200095
Published online July 28, 2020
Printed March 1, 2021
Yinong Yang
Beihang University
Abstract : 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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