Topological stability and pseudo-orbit tracing property of group actions

2017/02/08 by Nhan-Phu Chung, Nhan‐Phu Chung, Keonhee Lee · 3 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Advanced Topology and Set Theory

paper · pdf · doi:10.1090/proc/13654

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.

Cited by

• Topological Stability in Paired Dynamical Systems
• Topological Stability and Shadowing in Uniform Transformation Semigroups Modulo an Ideal
• Scale pressure for amenable group actions

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