Lower bounds for the local cyclicity for families of centers
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jde.2020.11.035 http://hdl.handle.net/11449/209826 |
Resumo: | In this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in [21], to prove that there exists a family of cubic centers, labeled by C D-31(12) in [25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields. (C) 2020 Elsevier Inc. All rights reserved. |
id |
UNSP_8759dd3f9443924478dd3c87f6e8a390 |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/209826 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
Lower bounds for the local cyclicity for families of centersSmall-amplitude limit cyclePolynomial vector fieldCenter cyclicityLyapunov constantsHigher-order developments and parallelizationIn this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in [21], to prove that there exists a family of cubic centers, labeled by C D-31(12) in [25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields. (C) 2020 Elsevier Inc. All rights reserved.Catalan AGAURSpanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacionEuropean CommunityConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Lleida, Dept Matemat, Avda Jaume II 69, Lleida 6925001, Catalonia, SpainUniv Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilCtr Recerca Matemat, Campus Bellaterra, Barcelona 08193, Catalonia, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilCatalan AGAUR: 2017SGR1617Catalan AGAUR: 2017SGR127Spanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacion: MTM2017-84383-PSpanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacion: PID2019-104658GB-I00European Community: H2020-MSCA-RISE-2017-777911CNPq: 200484/2015-0FAPESP: 2020/04717-0Elsevier B.V.Univ LleidaUniv Autonoma BarcelonaUniversidade Estadual Paulista (Unesp)Ctr Recerca MatematGine, JaumeGouveia, Luiz F. S. [UNESP]Torregrosa, Joan2021-06-25T12:30:34Z2021-06-25T12:30:34Z2021-02-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article309-331http://dx.doi.org/10.1016/j.jde.2020.11.035Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 275, p. 309-331, 2021.0022-0396http://hdl.handle.net/11449/20982610.1016/j.jde.2020.11.035WOS:000602880100011Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Differential Equationsinfo:eu-repo/semantics/openAccess2021-10-23T19:50:02Zoai:repositorio.unesp.br:11449/209826Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:05:55.403991Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Lower bounds for the local cyclicity for families of centers |
title |
Lower bounds for the local cyclicity for families of centers |
spellingShingle |
Lower bounds for the local cyclicity for families of centers Gine, Jaume Small-amplitude limit cycle Polynomial vector field Center cyclicity Lyapunov constants Higher-order developments and parallelization |
title_short |
Lower bounds for the local cyclicity for families of centers |
title_full |
Lower bounds for the local cyclicity for families of centers |
title_fullStr |
Lower bounds for the local cyclicity for families of centers |
title_full_unstemmed |
Lower bounds for the local cyclicity for families of centers |
title_sort |
Lower bounds for the local cyclicity for families of centers |
author |
Gine, Jaume |
author_facet |
Gine, Jaume Gouveia, Luiz F. S. [UNESP] Torregrosa, Joan |
author_role |
author |
author2 |
Gouveia, Luiz F. S. [UNESP] Torregrosa, Joan |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Univ Lleida Univ Autonoma Barcelona Universidade Estadual Paulista (Unesp) Ctr Recerca Matemat |
dc.contributor.author.fl_str_mv |
Gine, Jaume Gouveia, Luiz F. S. [UNESP] Torregrosa, Joan |
dc.subject.por.fl_str_mv |
Small-amplitude limit cycle Polynomial vector field Center cyclicity Lyapunov constants Higher-order developments and parallelization |
topic |
Small-amplitude limit cycle Polynomial vector field Center cyclicity Lyapunov constants Higher-order developments and parallelization |
description |
In this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in [21], to prove that there exists a family of cubic centers, labeled by C D-31(12) in [25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields. (C) 2020 Elsevier Inc. All rights reserved. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T12:30:34Z 2021-06-25T12:30:34Z 2021-02-25 |
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.jde.2020.11.035 Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 275, p. 309-331, 2021. 0022-0396 http://hdl.handle.net/11449/209826 10.1016/j.jde.2020.11.035 WOS:000602880100011 |
url |
http://dx.doi.org/10.1016/j.jde.2020.11.035 http://hdl.handle.net/11449/209826 |
identifier_str_mv |
Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 275, p. 309-331, 2021. 0022-0396 10.1016/j.jde.2020.11.035 WOS:000602880100011 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal Of Differential Equations |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
309-331 |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1808128460385681408 |