N-expansive homeomorphisms with the shadowing property

Detalhes bibliográficos
Autor(a) principal: Carvalho, B.
Data de Publicação: 2016
Outros Autores: Cordeiro, W.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: LOCUS Repositório Institucional da UFV
Texto Completo: https://doi.org/10.1016/j.jde.2016.06.003
http://www.locus.ufv.br/handle/123456789/21533
Resumo: We discuss the dynamics of n-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n∈N, we exhibit an n-expansive homeomorphism, which is not (n−1)-expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of n-expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing n-expansive homeomorphisms that are not expansive.
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spelling Carvalho, B.Cordeiro, W.2018-08-30T12:04:15Z2018-08-30T12:04:15Z2016-09-1500220396https://doi.org/10.1016/j.jde.2016.06.003http://www.locus.ufv.br/handle/123456789/21533We discuss the dynamics of n-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n∈N, we exhibit an n-expansive homeomorphism, which is not (n−1)-expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of n-expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing n-expansive homeomorphisms that are not expansive.engJournal of Differential Equationsv. 261, n. 6, p. 3734- 3755, september 2016Elsevier Inc.info:eu-repo/semantics/openAccessExpansiven-expansiveShadowingTransitiveLimit shadowingN-expansive homeomorphisms with the shadowing propertyinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdfTexto completoapplication/pdf297037https://locus.ufv.br//bitstream/123456789/21533/1/artigo.pdf10b732b3886ff6878ca55d8281e277c2MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/21533/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg4393https://locus.ufv.br//bitstream/123456789/21533/3/artigo.pdf.jpg53707c72838cb93c7541701d04298798MD53123456789/215332018-08-30 23:00:40.631oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-08-31T02:00:40LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false
dc.title.en.fl_str_mv N-expansive homeomorphisms with the shadowing property
title N-expansive homeomorphisms with the shadowing property
spellingShingle N-expansive homeomorphisms with the shadowing property
Carvalho, B.
Expansive
n-expansive
Shadowing
Transitive
Limit shadowing
title_short N-expansive homeomorphisms with the shadowing property
title_full N-expansive homeomorphisms with the shadowing property
title_fullStr N-expansive homeomorphisms with the shadowing property
title_full_unstemmed N-expansive homeomorphisms with the shadowing property
title_sort N-expansive homeomorphisms with the shadowing property
author Carvalho, B.
author_facet Carvalho, B.
Cordeiro, W.
author_role author
author2 Cordeiro, W.
author2_role author
dc.contributor.author.fl_str_mv Carvalho, B.
Cordeiro, W.
dc.subject.pt-BR.fl_str_mv Expansive
n-expansive
Shadowing
Transitive
Limit shadowing
topic Expansive
n-expansive
Shadowing
Transitive
Limit shadowing
description We discuss the dynamics of n-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n∈N, we exhibit an n-expansive homeomorphism, which is not (n−1)-expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of n-expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing n-expansive homeomorphisms that are not expansive.
publishDate 2016
dc.date.issued.fl_str_mv 2016-09-15
dc.date.accessioned.fl_str_mv 2018-08-30T12:04:15Z
dc.date.available.fl_str_mv 2018-08-30T12:04:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://doi.org/10.1016/j.jde.2016.06.003
http://www.locus.ufv.br/handle/123456789/21533
dc.identifier.issn.none.fl_str_mv 00220396
identifier_str_mv 00220396
url https://doi.org/10.1016/j.jde.2016.06.003
http://www.locus.ufv.br/handle/123456789/21533
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartofseries.pt-BR.fl_str_mv v. 261, n. 6, p. 3734- 3755, september 2016
dc.rights.driver.fl_str_mv Elsevier Inc.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Elsevier Inc.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Journal of Differential Equations
publisher.none.fl_str_mv Journal of Differential Equations
dc.source.none.fl_str_mv reponame:LOCUS Repositório Institucional da UFV
instname:Universidade Federal de Viçosa (UFV)
instacron:UFV
instname_str Universidade Federal de Viçosa (UFV)
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