Topological stability and shadowing property for group actions on metric spaces
J. Korean Math. Soc. Published online July 28, 2020
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 ∈ G such that Tg is expansive and has the shadowing property then T is topologically stable.
Keywords : Topological stability, shadowing property, expansiveness, group actions.