[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j200095

TOPOLOGICAL STABILITY AND SHADOWING PROPERTY FOR GROUP ACTIONS ON METRIC SPACES

Yang, Yinong (School of Mathematical Sciences Beihang University)

Publication Information

Journal of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 439-449 More about this Journal

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 if Tg is expansive and has the shadowing property, then T is topologically stable.

Keywords

Topological stability; shadowing property; expansiveness; group actions;

Citations & Related Records

Reference

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