VARIOUS SHADOWING PROPERTIES FOR INVERSE LIMIT SYSTEMS

Abstract

Let f : X → X be a continuous surjection of a compact metric space and let (Xf , (cid:101)f ) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f , if f has the asymptotic average, the average shadowing, the ergodic shadowing property then (cid:101)f is topologically transitive.

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