On the shadowing and limit shadowing properties

Noriaki Kawaguchi

Published 2017-10-01Version 1

In this paper, we deal with the relation between the shadowing property and the limit shadowing property. We prove that for any continuous self-map $f$ of a compact metric space, if $f$ has the limit shadowing property, then the restriction of $f$ to the non-wandering set satisfies the shadowing property. As an application, we prove the equivalence of the two shadowing properties for equicontinuous maps.