This article investigates under what conditions nontransitivity can coexist with the asymptotic average shadowing property. We show that there is a large class of maps satisfying both conditions simultaneously and that it is possible to find such examples even among maps on a compact interval. We also study the limit shadowing property and its relation to the asymptotic average shadowing property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-3,
author = {Marcin Kulczycki and Piotr Oprocha},
title = {Properties of dynamical systems with the asymptotic average shadowing property},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {35-52},
zbl = {1286.37007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-3}
}
Marcin Kulczycki; Piotr Oprocha. Properties of dynamical systems with the asymptotic average shadowing property. Fundamenta Mathematicae, Tome 215 (2011) pp. 35-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-3/