Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres

Detalhes bibliográficos
Autor(a) principal: Buzzi, Claudio A. [UNESP]
Data de Publicação: 2021
Outros Autores: Rodero, Ana Livia [UNESP], Torregrosa, Joan
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s00332-021-09751-z
http://hdl.handle.net/11449/222485
Resumo: The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify the centers of linear, quadratic homogeneous and a family of quadratic vector fields F⊂ X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F.
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spelling Centers and Limit Cycles of Vector Fields Defined on Invariant SpheresCenter-focus problemIntegrabilityLocal cyclicityVector fields on invariant spheresThe aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify the centers of linear, quadratic homogeneous and a family of quadratic vector fields F⊂ X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F.Agència de Gestió d'Ajuts Universitaris i de RecercaFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)H2020 European Research CouncilMinisterio de Ciencia, Innovación y UniversidadesInstituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)Departament de Matemàtiques Universitat Autònoma de BarcelonaCentre de Recerca Matemàtica, Campus de BellaterraInstituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)Agència de Gestió d'Ajuts Universitaris i de Recerca: 2017 SGR 1617FAPESP: 2017/08779-8FAPESP: 2019/00440- 7FAPESP: 2019/10269-3CNPq: CNPq 304798/2019- 3H2020 European Research Council: H2020-MSCA-RISE-2017- 777911Ministerio de Ciencia, Innovación y Universidades: PID2019-104658GB-I00Universidade Estadual Paulista (UNESP)Universitat Autònoma de BarcelonaCentre de Recerca MatemàticaBuzzi, Claudio A. [UNESP]Rodero, Ana Livia [UNESP]Torregrosa, Joan2022-04-28T19:44:54Z2022-04-28T19:44:54Z2021-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00332-021-09751-zJournal of Nonlinear Science, v. 31, n. 6, 2021.1432-14670938-8974http://hdl.handle.net/11449/22248510.1007/s00332-021-09751-z2-s2.0-85115725537Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Nonlinear Scienceinfo:eu-repo/semantics/openAccess2022-04-28T19:44:54Zoai:repositorio.unesp.br:11449/222485Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-28T19:44:54Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
title Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
spellingShingle Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
Buzzi, Claudio A. [UNESP]
Center-focus problem
Integrability
Local cyclicity
Vector fields on invariant spheres
title_short Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
title_full Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
title_fullStr Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
title_full_unstemmed Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
title_sort Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
author Buzzi, Claudio A. [UNESP]
author_facet Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Torregrosa, Joan
author_role author
author2 Rodero, Ana Livia [UNESP]
Torregrosa, Joan
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universitat Autònoma de Barcelona
Centre de Recerca Matemàtica
dc.contributor.author.fl_str_mv Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Torregrosa, Joan
dc.subject.por.fl_str_mv Center-focus problem
Integrability
Local cyclicity
Vector fields on invariant spheres
topic Center-focus problem
Integrability
Local cyclicity
Vector fields on invariant spheres
description The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify the centers of linear, quadratic homogeneous and a family of quadratic vector fields F⊂ X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F.
publishDate 2021
dc.date.none.fl_str_mv 2021-12-01
2022-04-28T19:44:54Z
2022-04-28T19:44:54Z
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/10.1007/s00332-021-09751-z
Journal of Nonlinear Science, v. 31, n. 6, 2021.
1432-1467
0938-8974
http://hdl.handle.net/11449/222485
10.1007/s00332-021-09751-z
2-s2.0-85115725537
url http://dx.doi.org/10.1007/s00332-021-09751-z
http://hdl.handle.net/11449/222485
identifier_str_mv Journal of Nonlinear Science, v. 31, n. 6, 2021.
1432-1467
0938-8974
10.1007/s00332-021-09751-z
2-s2.0-85115725537
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Nonlinear Science
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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_ 1803650022211846144

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