Orbitally symmetric systems with applications to planar centers

Detalhes bibliográficos
Autor(a) principal: Bastos, Jefferson L. R. [UNESP]
Data de Publicação: 2021
Outros Autores: Buzzi, Claudio A. [UNESP], Torregrosa, Joan
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.3934/cpaa.2021107
http://hdl.handle.net/11449/221891
Resumo: We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6; M(6) ≥ 48.
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spelling Orbitally symmetric systems with applications to planar centersCentersEquivarianceInvolutionLimit cyclesLocal cyclicityReversibilitySymmetryWe present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6; M(6) ≥ 48.Agència de Gestió d'Ajuts Universitaris i de RecercaDepartamento de Matemática Universidade Estadual Paulista Júlio de Mesquita FilhoDepartament de Matemátiques Universitat Autónoma de Barcelona, BellaterraCentre de Recerca Matemática Campus de Bellaterra, BellaterraDepartamento de Matemática Universidade Estadual Paulista Júlio de Mesquita FilhoAgència de Gestió d'Ajuts Universitaris i de Recerca: 2017Universidade Estadual Paulista (UNESP)Universitat Autónoma de BarcelonaCentre de Recerca MatemáticaBastos, Jefferson L. R. [UNESP]Buzzi, Claudio A. [UNESP]Torregrosa, Joan2022-04-28T19:41:06Z2022-04-28T19:41:06Z2021-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3301-3329http://dx.doi.org/10.3934/cpaa.2021107Communications on Pure and Applied Analysis, v. 20, n. 10, p. 3301-3329, 2021.1553-52581534-0392http://hdl.handle.net/11449/22189110.3934/cpaa.20211072-s2.0-85109064608Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications on Pure and Applied Analysisinfo:eu-repo/semantics/openAccess2022-04-28T19:41:06Zoai:repositorio.unesp.br:11449/221891Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:52:44.606673Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Orbitally symmetric systems with applications to planar centers
title Orbitally symmetric systems with applications to planar centers
spellingShingle Orbitally symmetric systems with applications to planar centers
Bastos, Jefferson L. R. [UNESP]
Centers
Equivariance
Involution
Limit cycles
Local cyclicity
Reversibility
Symmetry
title_short Orbitally symmetric systems with applications to planar centers
title_full Orbitally symmetric systems with applications to planar centers
title_fullStr Orbitally symmetric systems with applications to planar centers
title_full_unstemmed Orbitally symmetric systems with applications to planar centers
title_sort Orbitally symmetric systems with applications to planar centers
author Bastos, Jefferson L. R. [UNESP]
author_facet Bastos, Jefferson L. R. [UNESP]
Buzzi, Claudio A. [UNESP]
Torregrosa, Joan
author_role author
author2 Buzzi, Claudio A. [UNESP]
Torregrosa, Joan
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universitat Autónoma de Barcelona
Centre de Recerca Matemática
dc.contributor.author.fl_str_mv Bastos, Jefferson L. R. [UNESP]
Buzzi, Claudio A. [UNESP]
Torregrosa, Joan
dc.subject.por.fl_str_mv Centers
Equivariance
Involution
Limit cycles
Local cyclicity
Reversibility
Symmetry
topic Centers
Equivariance
Involution
Limit cycles
Local cyclicity
Reversibility
Symmetry
description We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6; M(6) ≥ 48.
publishDate 2021
dc.date.none.fl_str_mv 2021-10-01
2022-04-28T19:41:06Z
2022-04-28T19:41:06Z
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/10.3934/cpaa.2021107
Communications on Pure and Applied Analysis, v. 20, n. 10, p. 3301-3329, 2021.
1553-5258
1534-0392
http://hdl.handle.net/11449/221891
10.3934/cpaa.2021107
2-s2.0-85109064608
url http://dx.doi.org/10.3934/cpaa.2021107
http://hdl.handle.net/11449/221891
identifier_str_mv Communications on Pure and Applied Analysis, v. 20, n. 10, p. 3301-3329, 2021.
1553-5258
1534-0392
10.3934/cpaa.2021107
2-s2.0-85109064608
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Communications on Pure and Applied Analysis
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 3301-3329
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_ 1808128714388537344

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