Periodic shadowing and $\Omega$-stability

Abstract

We show that the following three properties of a diffeomorphism $f$ of a smooth closed manifold are equivalent: (i) $f$ belongs to the $C^1$-interior of the set of diffeomorphisms having periodic shadowing property; (ii) $f$ has Lipschitz periodic shadowing property; (iii) $f$ is $\Omega$-stable.