SHADOWABLE POINTS FOR FINITELY GENERATED GROUP ACTIONS

In this paper we introduce the notion of shadowable points for finitely generated group actions on compact metric spaace and prove that the set of shadowable points is invariant and Borel set and if chain recurrent set contained shadowable point set then it coincide with nonwandering set. Moreover an action T ∈ Act(G, X) has the shadowing property if and only if every point is shadowable.