SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

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.