On the shadowing and limit shadowing properties
Volume 249 / 2020
Fundamenta Mathematicae 249 (2020), 21-35
MSC: 37C50, 54H20, 37B20.
DOI: 10.4064/fm552-4-2019
Published online: 23 August 2019
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.
