Gluing orbit property and partial hyperbolicity

Detalhes bibliográficos
Autor(a) principal: Bomfim, Thiago
Data de Publicação: 2021
Outros Autores: Torres, M. J., Varandas, Paulo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/75204
Resumo: This article is a follow up of our recent works [7, 8], and here we discuss the relation between the gluing orbit property and partial hyperbolicity. First we prove that a partially hyperbolic diffeomorphism with two saddles with different index, and such that the stable manifold of one of these saddles coincides with the strongly stable leaf does not satisfy the gluing orbit property. In particular, the examples of C 1 -robustly transitive diffeomorphisms introduced by Man˜e [ ´ 20] do not satisfy the gluing orbit property. We also construct some families of partially hyperbolic skew-products satisfying the gluing orbit property and derive some estimates on their quantitative recurrence.
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spelling Gluing orbit property and partial hyperbolicityGluing orbit propertySpecificationPartial hyperbolicityRecurrenceCiências Naturais::MatemáticasScience & TechnologyThis article is a follow up of our recent works [7, 8], and here we discuss the relation between the gluing orbit property and partial hyperbolicity. First we prove that a partially hyperbolic diffeomorphism with two saddles with different index, and such that the stable manifold of one of these saddles coincides with the strongly stable leaf does not satisfy the gluing orbit property. In particular, the examples of C 1 -robustly transitive diffeomorphisms introduced by Man˜e [ ´ 20] do not satisfy the gluing orbit property. We also construct some families of partially hyperbolic skew-products satisfying the gluing orbit property and derive some estimates on their quantitative recurrence.MJT was partially supported by FCT (Fundacao para a Ciencia e a Tecnologia-Portugal) within the Projects UIDB/00013/2020 and UIDP/00013/2020 and by the Project 'New trends in Lyapunov exponents' (PTDC/MAT-PUR/29126/2017). PV was partially supported by CNPq-Brazil, by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020, and by Fundacao para a Ciencia e a Tecnologia (FCT) - Portugal, through the grant CEECIND/03721/2017 of the Stimulus of Scientific Employment, Individual Support 2017 Call.ElsevierUniversidade do MinhoBomfim, ThiagoTorres, M. J.Varandas, Paulo20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/75204eng0022-039610.1016/j.jde.2020.09.040https://www.sciencedirect.com/science/article/abs/pii/S0022039620305350?via%3Dihubinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:46:09Zoai:repositorium.sdum.uminho.pt:1822/75204Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:44:08.793632Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Gluing orbit property and partial hyperbolicity
title Gluing orbit property and partial hyperbolicity
spellingShingle Gluing orbit property and partial hyperbolicity
Bomfim, Thiago
Gluing orbit property
Specification
Partial hyperbolicity
Recurrence
Ciências Naturais::Matemáticas
Science & Technology
title_short Gluing orbit property and partial hyperbolicity
title_full Gluing orbit property and partial hyperbolicity
title_fullStr Gluing orbit property and partial hyperbolicity
title_full_unstemmed Gluing orbit property and partial hyperbolicity
title_sort Gluing orbit property and partial hyperbolicity
author Bomfim, Thiago
author_facet Bomfim, Thiago
Torres, M. J.
Varandas, Paulo
author_role author
author2 Torres, M. J.
Varandas, Paulo
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Bomfim, Thiago
Torres, M. J.
Varandas, Paulo
dc.subject.por.fl_str_mv Gluing orbit property
Specification
Partial hyperbolicity
Recurrence
Ciências Naturais::Matemáticas
Science & Technology
topic Gluing orbit property
Specification
Partial hyperbolicity
Recurrence
Ciências Naturais::Matemáticas
Science & Technology
description This article is a follow up of our recent works [7, 8], and here we discuss the relation between the gluing orbit property and partial hyperbolicity. First we prove that a partially hyperbolic diffeomorphism with two saddles with different index, and such that the stable manifold of one of these saddles coincides with the strongly stable leaf does not satisfy the gluing orbit property. In particular, the examples of C 1 -robustly transitive diffeomorphisms introduced by Man˜e [ ´ 20] do not satisfy the gluing orbit property. We also construct some families of partially hyperbolic skew-products satisfying the gluing orbit property and derive some estimates on their quantitative recurrence.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
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 http://hdl.handle.net/1822/75204
url http://hdl.handle.net/1822/75204
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-0396
10.1016/j.jde.2020.09.040
https://www.sciencedirect.com/science/article/abs/pii/S0022039620305350?via%3Dihub
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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