Topological stability and shadowing property for group actions on metric spaces
J. Korean Math. Soc.
Published online July 28, 2020
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 ∈ G such that Tg 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
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