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