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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-3-4,
author = {Marcin Kulczycki and Dominik Kwietniak and Piotr Oprocha},
title = {On almost specification and average shadowing properties},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {241-278},
zbl = {06280649},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-3-4}
}
Marcin Kulczycki; Dominik Kwietniak; Piotr Oprocha. On almost specification and average shadowing properties. Fundamenta Mathematicae, Tome 227 (2014) pp. 241-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-3-4/