TOPOLOGICAL STABILITY AND PSEUDO-ORBIT TRACING PROPERTY OF GROUP ACTIONS.

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 pseudoorbit 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. [ABSTRACT FROM AUTHOR]