We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-2,
author = {Andrew D. Barwell and Chris Good and Piotr Oprocha},
title = {Shadowing and expansivity in subspaces},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {223-243},
zbl = {06113307},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-2}
}
Andrew D. Barwell; Chris Good; Piotr Oprocha. Shadowing and expansivity in subspaces. Fundamenta Mathematicae, Tome 219 (2012) pp. 223-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-2/