On the shadowing and limit shadowing properties

Abstract

We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space 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.

References in corpus (3)

• On homeomorphisms with the two-sided limit shadowing property
• Properties of invariant measures in dynamical systems with the shadowing property
• Shadowing, asymptotic shadowing and s-limit shadowing

Cited by in corpus (2)

• Suspensions of homeomorphisms with the two-sided limit shadowing property
• Distributionally chaotic maps are $C^0$-dense