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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.
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참고문헌 (9)
참고문헌 신청
N.-P. Chung / 2018 / Topological stability and pseudo-orbit tracing property of group actions / Proc. Amer. Math. Soc 146(3):1047~1057
Keonhee Lee / 2017 / Topological stability and pseudo-orbit tracing property for expansive measures / Journal of Differential Equations 262(6):3467~3487
Keonhee Lee / 2018 / Topological stability and spectral decomposition for homeomorphisms on noncompact spaces / Discrete & Continuous Dynamical Systems - A 38(5):2487~2503
Piotr Oprocha / 2008 / Shadowing in multi-dimensional shift spaces / Colloquium Mathematicum 110(2):451~460
Alexey V. Osipov / 2014 / Shadowing for actions of some finitely generated groups / Dynamical Systems 29(3):337~351
Keonhee Lee / 2017 / Topological stability and pseudo-orbit tracing property for expansive measures / Journal of Differential Equations 262(6):3467~3487
Keonhee Lee / 2018 / Topological stability and spectral decomposition for homeomorphisms on noncompact spaces / Discrete & Continuous Dynamical Systems - A 38(5):2487~2503
Piotr Oprocha / 2008 / Shadowing in multi-dimensional shift spaces / Colloquium Mathematicum 110(2):451~460
Alexey V. Osipov / 2014 / Shadowing for actions of some finitely generated groups / Dynamical Systems 29(3):337~351
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