Topological stability and shadowing property for group actions on metric spaces
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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.
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.
참고문헌 (9)
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