Lower bounds for the local cyclicity of centers using high order developments and parallelization
Autor(a) principal: | |
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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.2020.08.027 http://hdl.handle.net/11449/209748 |
Resumo: | We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. This technique is useful to study lower bounds for the local cyclicity of centers. We denote by M(n) the maximum number of limit cycles bifurcating from the origin via a degenerate Hopf bifurcation for a polynomial vector field of degree n. We get lower bounds for the local cyclicity of some known cubic centers and we prove that M(4) >= 20, M(5) >= 33, M(7) >= 61, M(8) >= 76, and M(9) >= 88. (C) 2020 Elsevier Inc. All rights reserved. |
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Repositório Institucional da UNESP |
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Lower bounds for the local cyclicity of centers using high order developments and parallelizationSmall-amplitude limit cyclePolynomial vector fieldCenter cyclicityLyapunov constantsHigher-order developments and parallelizationWe are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. This technique is useful to study lower bounds for the local cyclicity of centers. We denote by M(n) the maximum number of limit cycles bifurcating from the origin via a degenerate Hopf bifurcation for a polynomial vector field of degree n. We get lower bounds for the local cyclicity of some known cubic centers and we prove that M(4) >= 20, M(5) >= 33, M(7) >= 61, M(8) >= 76, and M(9) >= 88. (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 Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilCatalan AGAUR: 2017SGR1617Spanish Ministerio de Ciencia, Innovacion y Universidades - Agencia estatal de investigacion: MTM201677278-PEuropean Community: H2020-MSCA-RISE-2017-777911CNPq: 200484/2015-0FAPESP: 2020/04717-0Elsevier B.V.Univ Autonoma BarcelonaUniversidade Estadual Paulista (Unesp)Gouveia, Luiz F. S. [UNESP]Torregrosa, Joan2021-06-25T12:27:56Z2021-06-25T12:27:56Z2021-01-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article447-479http://dx.doi.org/10.1016/j.jde.2020.08.027Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 271, p. 447-479, 2021.0022-0396http://hdl.handle.net/11449/20974810.1016/j.jde.2020.08.027WOS:000596071000016Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Differential Equationsinfo:eu-repo/semantics/openAccess2021-10-23T19:49:59Zoai:repositorio.unesp.br:11449/209748Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:03:06.798447Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
title |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
spellingShingle |
Lower bounds for the local cyclicity of centers using high order developments and parallelization Gouveia, Luiz F. S. [UNESP] Small-amplitude limit cycle Polynomial vector field Center cyclicity Lyapunov constants Higher-order developments and parallelization |
title_short |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
title_full |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
title_fullStr |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
title_full_unstemmed |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
title_sort |
Lower bounds for the local cyclicity of centers using high order developments and parallelization |
author |
Gouveia, Luiz F. S. [UNESP] |
author_facet |
Gouveia, Luiz F. S. [UNESP] Torregrosa, Joan |
author_role |
author |
author2 |
Torregrosa, Joan |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Univ Autonoma Barcelona Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
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 |
We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. This technique is useful to study lower bounds for the local cyclicity of centers. We denote by M(n) the maximum number of limit cycles bifurcating from the origin via a degenerate Hopf bifurcation for a polynomial vector field of degree n. We get lower bounds for the local cyclicity of some known cubic centers and we prove that M(4) >= 20, M(5) >= 33, M(7) >= 61, M(8) >= 76, and M(9) >= 88. (C) 2020 Elsevier Inc. All rights reserved. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T12:27:56Z 2021-06-25T12:27:56Z 2021-01-15 |
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.2020.08.027 Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 271, p. 447-479, 2021. 0022-0396 http://hdl.handle.net/11449/209748 10.1016/j.jde.2020.08.027 WOS:000596071000016 |
url |
http://dx.doi.org/10.1016/j.jde.2020.08.027 http://hdl.handle.net/11449/209748 |
identifier_str_mv |
Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 271, p. 447-479, 2021. 0022-0396 10.1016/j.jde.2020.08.027 WOS:000596071000016 |
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 |
447-479 |
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_ |
1808128888853757952 |