Cyclicity of rigid centres on centre manifolds of three-dimensional systems

Bibliographic Details
Main Author: Pessoa, Claudio [UNESP]
Publication Date: 2023
Other Authors: Queiroz, Lucas [UNESP], Ribeiro, Jarne D.
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1017/prm.2023.2
http://hdl.handle.net/11449/245231
Summary: We work with polynomial three-dimensional rigid differential systems. Using the Lyapunov constants, we obtain lower bounds for the cyclicity of the known rigid centres on their centre manifolds. Moreover, we obtain an example of a quadratic rigid centre from which is possible to bifurcate 13 limit cycles, which is a new lower bound for three-dimensional quadratic systems.
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spelling Cyclicity of rigid centres on centre manifolds of three-dimensional systemsLimit cyclesrigid centresHopf singularitiescentre manifoldsthree-dimensional systemsLyapunov constantsWe work with polynomial three-dimensional rigid differential systems. Using the Lyapunov constants, we obtain lower bounds for the cyclicity of the known rigid centres on their centre manifolds. Moreover, we obtain an example of a quadratic rigid centre from which is possible to bifurcate 13 limit cycles, which is a new lower bound for three-dimensional quadratic systems.Funda��o de Amparo � Pesquisa do Estado de S�o Paulo (FAPESP)Instituto Federal de Educacao, Ciencia e Tecnologia do Sul de Minas Gerais - IFSULDEMINASUniv Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, R Cristovao Colombo 2265, BR-15054000 Campinas, BrazilInst Fed Educ Ciencia & Tecnol Minas Gerais IFSULD, R Mario Ribola 409,Penha 2, BR-37903358 Passos, MG, BrazilUniv Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, R Cristovao Colombo 2265, BR-15054000 Campinas, BrazilFAPESP: 19/13040-7Cambridge Univ PressUniversidade Estadual Paulista (UNESP)Inst Fed Educ Ciencia & Tecnol Minas Gerais IFSULDPessoa, Claudio [UNESP]Queiroz, Lucas [UNESP]Ribeiro, Jarne D.2023-07-29T11:49:04Z2023-07-29T11:49:04Z2023-02-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article13http://dx.doi.org/10.1017/prm.2023.2Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 13 p., 2023.0308-2105http://hdl.handle.net/11449/24523110.1017/prm.2023.2WOS:000940495100001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings Of The Royal Society Of Edinburgh Section A-mathematicsinfo:eu-repo/semantics/openAccess2025-04-03T18:18:11Zoai:repositorio.unesp.br:11449/245231Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-03T18:18:11Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Cyclicity of rigid centres on centre manifolds of three-dimensional systems
title Cyclicity of rigid centres on centre manifolds of three-dimensional systems
spellingShingle Cyclicity of rigid centres on centre manifolds of three-dimensional systems
Pessoa, Claudio [UNESP]
Limit cycles
rigid centres
Hopf singularities
centre manifolds
three-dimensional systems
Lyapunov constants
title_short Cyclicity of rigid centres on centre manifolds of three-dimensional systems
title_full Cyclicity of rigid centres on centre manifolds of three-dimensional systems
title_fullStr Cyclicity of rigid centres on centre manifolds of three-dimensional systems
title_full_unstemmed Cyclicity of rigid centres on centre manifolds of three-dimensional systems
title_sort Cyclicity of rigid centres on centre manifolds of three-dimensional systems
author Pessoa, Claudio [UNESP]
author_facet Pessoa, Claudio [UNESP]
Queiroz, Lucas [UNESP]
Ribeiro, Jarne D.
author_role author
author2 Queiroz, Lucas [UNESP]
Ribeiro, Jarne D.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Inst Fed Educ Ciencia & Tecnol Minas Gerais IFSULD
dc.contributor.author.fl_str_mv Pessoa, Claudio [UNESP]
Queiroz, Lucas [UNESP]
Ribeiro, Jarne D.
dc.subject.por.fl_str_mv Limit cycles
rigid centres
Hopf singularities
centre manifolds
three-dimensional systems
Lyapunov constants
topic Limit cycles
rigid centres
Hopf singularities
centre manifolds
three-dimensional systems
Lyapunov constants
description We work with polynomial three-dimensional rigid differential systems. Using the Lyapunov constants, we obtain lower bounds for the cyclicity of the known rigid centres on their centre manifolds. Moreover, we obtain an example of a quadratic rigid centre from which is possible to bifurcate 13 limit cycles, which is a new lower bound for three-dimensional quadratic systems.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-29T11:49:04Z
2023-07-29T11:49:04Z
2023-02-09
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/10.1017/prm.2023.2
Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 13 p., 2023.
0308-2105
http://hdl.handle.net/11449/245231
10.1017/prm.2023.2
WOS:000940495100001
url http://dx.doi.org/10.1017/prm.2023.2
http://hdl.handle.net/11449/245231
identifier_str_mv Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 13 p., 2023.
0308-2105
10.1017/prm.2023.2
WOS:000940495100001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Proceedings Of The Royal Society Of Edinburgh Section A-mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 13
dc.publisher.none.fl_str_mv Cambridge Univ Press
publisher.none.fl_str_mv Cambridge Univ Press
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 repositoriounesp@unesp.br
_version_ 1854947736473829376

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