On the Closing Lemma for planar piecewise smooth vector fields

Detalhes bibliográficos
Autor(a) principal: de Carvalho, Tiago [UNESP]
Data de Publicação: 2016
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.matpur.2016.04.006
http://hdl.handle.net/11449/169073
Resumo: A large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points for the context of planar piecewise smooth vector fields. A global bifurcation analysis of a special family of piecewise smooth vector fields presenting a nonwandering set with nontrivial recurrence is performed. As a consequence, we are able to say that the Classical and the Improved Closing Lemmas are false for this scenario.
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spelling On the Closing Lemma for planar piecewise smooth vector fieldsClosing LemmaNonsmooth vector fieldNonwandering pointsRecurrent pointsA large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points for the context of planar piecewise smooth vector fields. A global bifurcation analysis of a special family of piecewise smooth vector fields presenting a nonwandering set with nontrivial recurrence is performed. As a consequence, we are able to say that the Classical and the Improved Closing Lemmas are false for this scenario.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FC–UNESP, CEP 17033–360FC–UNESP, CEP 17033–360CAPES: 1576689FAPESP: 2014/02134-7CNPq: 443302/2014-6CAPES: 88881.030454/2013-01Universidade Estadual Paulista (Unesp)de Carvalho, Tiago [UNESP]2018-12-11T16:44:13Z2018-12-11T16:44:13Z2016-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1174-1185application/pdfhttp://dx.doi.org/10.1016/j.matpur.2016.04.006Journal des Mathematiques Pures et Appliquees, v. 106, n. 6, p. 1174-1185, 2016.0021-7824http://hdl.handle.net/11449/16907310.1016/j.matpur.2016.04.0062-s2.0-849927153292-s2.0-84992715329.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal des Mathematiques Pures et Appliquees3,571info:eu-repo/semantics/openAccess2023-12-16T06:17:05Zoai:repositorio.unesp.br:11449/169073Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:27:37.586637Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On the Closing Lemma for planar piecewise smooth vector fields
title On the Closing Lemma for planar piecewise smooth vector fields
spellingShingle On the Closing Lemma for planar piecewise smooth vector fields
de Carvalho, Tiago [UNESP]
Closing Lemma
Nonsmooth vector field
Nonwandering points
Recurrent points
title_short On the Closing Lemma for planar piecewise smooth vector fields
title_full On the Closing Lemma for planar piecewise smooth vector fields
title_fullStr On the Closing Lemma for planar piecewise smooth vector fields
title_full_unstemmed On the Closing Lemma for planar piecewise smooth vector fields
title_sort On the Closing Lemma for planar piecewise smooth vector fields
author de Carvalho, Tiago [UNESP]
author_facet de Carvalho, Tiago [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv de Carvalho, Tiago [UNESP]
dc.subject.por.fl_str_mv Closing Lemma
Nonsmooth vector field
Nonwandering points
Recurrent points
topic Closing Lemma
Nonsmooth vector field
Nonwandering points
Recurrent points
description A large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points for the context of planar piecewise smooth vector fields. A global bifurcation analysis of a special family of piecewise smooth vector fields presenting a nonwandering set with nontrivial recurrence is performed. As a consequence, we are able to say that the Classical and the Improved Closing Lemmas are false for this scenario.
publishDate 2016
dc.date.none.fl_str_mv 2016-12-01
2018-12-11T16:44:13Z
2018-12-11T16:44:13Z
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://dx.doi.org/10.1016/j.matpur.2016.04.006
Journal des Mathematiques Pures et Appliquees, v. 106, n. 6, p. 1174-1185, 2016.
0021-7824
http://hdl.handle.net/11449/169073
10.1016/j.matpur.2016.04.006
2-s2.0-84992715329
2-s2.0-84992715329.pdf
url http://dx.doi.org/10.1016/j.matpur.2016.04.006
http://hdl.handle.net/11449/169073
identifier_str_mv Journal des Mathematiques Pures et Appliquees, v. 106, n. 6, p. 1174-1185, 2016.
0021-7824
10.1016/j.matpur.2016.04.006
2-s2.0-84992715329
2-s2.0-84992715329.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal des Mathematiques Pures et Appliquees
3,571
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1174-1185
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129204766638080

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