On Periodic Shadowing Property

On Periodic Shadowing Property

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodi...

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Bibliographic Details
Main Author: Ali Darabi
Format: Article
Language:English
Published: University of Maragheh 2019-04-01
Series:Sahand Communications in Mathematical Analysis
Subjects:
Periodic shadowing
Shadowing
Chain transitive
Distal
Online Access:http://scma.maragheh.ac.ir/article_34858_a4fd5aa56afc0bc5a20ffba49c31265a.pdf
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spelling doaj-b3a38f16ee034e2591a9f163da12831b2020-11-25T02:15:32ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-04-01141637210.22130/scma.2018.69088.27034858On Periodic Shadowing PropertyAli Darabi0Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahvaz, P.O. Box 61357-43135, Ahvaz, Iran.In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chaotic in the sense of Li-Yorke. Moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.http://scma.maragheh.ac.ir/article_34858_a4fd5aa56afc0bc5a20ffba49c31265a.pdfPeriodic shadowingShadowingChain transitiveDistal
collection DOAJ
language English
format Article
sources DOAJ
author Ali Darabi
spellingShingle Ali Darabi
On Periodic Shadowing Property
Sahand Communications in Mathematical Analysis
Periodic shadowing
Shadowing
Chain transitive
Distal
author_facet Ali Darabi
author_sort Ali Darabi
title On Periodic Shadowing Property
title_short On Periodic Shadowing Property
title_full On Periodic Shadowing Property
title_fullStr On Periodic Shadowing Property
title_full_unstemmed On Periodic Shadowing Property
title_sort on periodic shadowing property
publisher University of Maragheh
series Sahand Communications in Mathematical Analysis
issn 2322-5807
2423-3900
publishDate 2019-04-01
description In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chaotic in the sense of Li-Yorke. Moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.
topic Periodic shadowing
Shadowing
Chain transitive
Distal
url http://scma.maragheh.ac.ir/article_34858_a4fd5aa56afc0bc5a20ffba49c31265a.pdf
work_keys_str_mv AT alidarabi onperiodicshadowingproperty
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