Topological stability and pseudo-orbit tracing property of group actions

Chung, Nhan-Phu; Lee, Keonhee

doi:10.1090/proc/13654

Topological stability and pseudo-orbit tracing property of group actions
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by Nhan-Phu Chung and Keonhee Lee

Proc. Amer. Math. Soc. 146 (2018), 1047-1057

DOI: https://doi.org/10.1090/proc/13654

Published electronically: November 29, 2017

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Abstract:

In this paper we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property, then it is topologicaly stable. This represents a group action version of P. Walter’s stability theorem [Lecture Notes in Math., vol. 668, Springer, 1978, pp. 231–244]. Moreover we give a class of group actions with topological stability or pseudo-orbit tracing property. In particular, we establish a characterization of subshifts of finite type over finitely generated groups in terms of the pseudo-orbit tracing property.

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