On almost specification and average shadowing properties

Marcin Kulczycki, Dominik Kwietniak, and Piotr Oprocha. "On almost specification and average shadowing properties." Fundamenta Mathematicae 224.3 (2014): 241-278. <http://eudml.org/doc/282821>.

@article{MarcinKulczycki2014,
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.},
author = {Marcin Kulczycki, Dominik Kwietniak, Piotr Oprocha},
journal = {Fundamenta Mathematicae},
keywords = {average shadowing property; asymptotic average shadowing property; shadowing; pseudo-orbit; chain mixing},
language = {eng},
number = {3},
pages = {241-278},
title = {On almost specification and average shadowing properties},
url = {http://eudml.org/doc/282821},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Marcin Kulczycki
AU - Dominik Kwietniak
AU - Piotr Oprocha
TI - On almost specification and average shadowing properties
JO - Fundamenta Mathematicae
PY - 2014
VL - 224
IS - 3
SP - 241
EP - 278
AB - 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.
LA - eng
KW - average shadowing property; asymptotic average shadowing property; shadowing; pseudo-orbit; chain mixing
UR - http://eudml.org/doc/282821
ER -