Shadowing Property on Finitely Generated Group Actions

Abstract

In this paper, we study shadowing property for actions of finitely generated groups and show that conjugacy preserves shadowing property and in the actions with shadowing property, topologically transitive is equivalent to chain transitive and the set of non-wandering points is equal to the set of chain recurrent points. For actions of finitely generated free groups, we prove that on a compact metric space of non-zero dimension, every action with chain transitive and shadowing property is sensitive.