Path formulation for multiparameter D3-equivariant bifurcation problems

Detalhes bibliográficos
Autor(a) principal: Furter, Jacques-Élie
Data de Publicação: 2010
Outros Autores: Sitta, Angela Maria [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.5802/aif.2558
http://hdl.handle.net/11449/71965
Resumo: We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.
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spelling Path formulation for multiparameter D3-equivariant bifurcation problems1:1-resonanceDegenerate bifurcationEquivariant bifurcationPath formulationReversible systemsSingularity theorySubharmonic bifurcationWe implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.Brunel University Department of Mathematical Sciences, Uxbridge UB8 3PHUniversidade Estadual Paulista - UNESP Departamento de Matemática - IBILCE Campus de São José, Rio Preto - SPUniversidade Estadual Paulista - UNESP Departamento de Matemática - IBILCE Campus de São José, Rio Preto - SPBrunel UniversityUniversidade Estadual Paulista (Unesp)Furter, Jacques-ÉlieSitta, Angela Maria [UNESP]2014-05-27T11:24:50Z2014-05-27T11:24:50Z2010-11-22info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1363-1400http://dx.doi.org/10.5802/aif.2558Annales de l'Institut Fourier, v. 60, n. 4, p. 1363-1400, 2010.0373-0956http://hdl.handle.net/11449/7196510.5802/aif.25582-s2.0-78349232386Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAnnales de l'Institut Fourier0.6381,703info:eu-repo/semantics/openAccess2021-10-22T21:54:39Zoai:repositorio.unesp.br:11449/71965Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-22T21:54:39Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Path formulation for multiparameter D3-equivariant bifurcation problems
title Path formulation for multiparameter D3-equivariant bifurcation problems
spellingShingle Path formulation for multiparameter D3-equivariant bifurcation problems
Furter, Jacques-Élie
1:1-resonance
Degenerate bifurcation
Equivariant bifurcation
Path formulation
Reversible systems
Singularity theory
Subharmonic bifurcation
title_short Path formulation for multiparameter D3-equivariant bifurcation problems
title_full Path formulation for multiparameter D3-equivariant bifurcation problems
title_fullStr Path formulation for multiparameter D3-equivariant bifurcation problems
title_full_unstemmed Path formulation for multiparameter D3-equivariant bifurcation problems
title_sort Path formulation for multiparameter D3-equivariant bifurcation problems
author Furter, Jacques-Élie
author_facet Furter, Jacques-Élie
Sitta, Angela Maria [UNESP]
author_role author
author2 Sitta, Angela Maria [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Brunel University
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Furter, Jacques-Élie
Sitta, Angela Maria [UNESP]
dc.subject.por.fl_str_mv 1:1-resonance
Degenerate bifurcation
Equivariant bifurcation
Path formulation
Reversible systems
Singularity theory
Subharmonic bifurcation
topic 1:1-resonance
Degenerate bifurcation
Equivariant bifurcation
Path formulation
Reversible systems
Singularity theory
Subharmonic bifurcation
description We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.
publishDate 2010
dc.date.none.fl_str_mv 2010-11-22
2014-05-27T11:24:50Z
2014-05-27T11:24:50Z
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/10.5802/aif.2558
Annales de l'Institut Fourier, v. 60, n. 4, p. 1363-1400, 2010.
0373-0956
http://hdl.handle.net/11449/71965
10.5802/aif.2558
2-s2.0-78349232386
url http://dx.doi.org/10.5802/aif.2558
http://hdl.handle.net/11449/71965
identifier_str_mv Annales de l'Institut Fourier, v. 60, n. 4, p. 1363-1400, 2010.
0373-0956
10.5802/aif.2558
2-s2.0-78349232386
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Annales de l'Institut Fourier
0.638
1,703
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1363-1400
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_ 1797789583307440128

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