On almost specification and average shadowing properties
Volume 224 / 2014
Fundamenta Mathematicae 224 (2014), 241-278
MSC: Primary 37B05; Secondary 34D05, 37D45.
DOI: 10.4064/fm224-3-4
Abstract
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.
