Abstract:In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system (X, f ) has shadowing, then it is recurrent if and only if it is minimal. Furthermore, we show that a uniformly rigid system (X, f ) has shadowing if and only if X is totally disconnected and use this to demonstrate the existence of a space X for which no surjective system (X, f ) has shadowing. We further refin… Show more
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