On homeomorphisms with the two-sided limit shadowing property

Bibliographic description

punktacja MEiN [2014 A]: 35

title:	On homeomorphisms with the two-sided limit shadowing property
author:	Carvalho Bernardo, Kwietniak Dominik
journal title:	Journal of Mathematical Analysis and Applications
volume:	420
issue:	1
date of publication :	2014
pages:	801-813
ISSN:	0022-247X
eISSN:	1096-0813
DOI:	10.1016/j.jmaa.2014.06.011
language:	English
journal language:	English
abstract in English:	We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper

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