SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

Abstract

Let f : X → X be a continuous surjection of a compact metric space X and let σf : Xf → Xf be the shift map on the inverse limit space Xf constructed by f . We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then σf also has the same properties.

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