Complete Set of Invariants for a Bykov Attractor

Detalhes bibliográficos
Autor(a) principal: Maria Pires de Carvalho
Data de Publicação: 2018
Outros Autores: Alexandre A. P. Rodrigues
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/10216/110430
Resumo: In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behavior and, from the asymptotic properties of these nonconverging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.
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spelling Complete Set of Invariants for a Bykov AttractorMatemática, MatemáticaMathematics, MathematicsIn this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behavior and, from the asymptotic properties of these nonconverging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.2018-062018-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/110430eng1560-354710.1134/s1560354718030012Maria Pires de CarvalhoAlexandre A. P. Rodriguesinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T14:11:03Zoai:repositorio-aberto.up.pt:10216/110430Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:56:35.586766Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Complete Set of Invariants for a Bykov Attractor
title Complete Set of Invariants for a Bykov Attractor
spellingShingle Complete Set of Invariants for a Bykov Attractor
Maria Pires de Carvalho
Matemática, Matemática
Mathematics, Mathematics
title_short Complete Set of Invariants for a Bykov Attractor
title_full Complete Set of Invariants for a Bykov Attractor
title_fullStr Complete Set of Invariants for a Bykov Attractor
title_full_unstemmed Complete Set of Invariants for a Bykov Attractor
title_sort Complete Set of Invariants for a Bykov Attractor
author Maria Pires de Carvalho
author_facet Maria Pires de Carvalho
Alexandre A. P. Rodrigues
author_role author
author2 Alexandre A. P. Rodrigues
author2_role author
dc.contributor.author.fl_str_mv Maria Pires de Carvalho
Alexandre A. P. Rodrigues
dc.subject.por.fl_str_mv Matemática, Matemática
Mathematics, Mathematics
topic Matemática, Matemática
Mathematics, Mathematics
description In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behavior and, from the asymptotic properties of these nonconverging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.
publishDate 2018
dc.date.none.fl_str_mv 2018-06
2018-06-01T00:00:00Z
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 https://hdl.handle.net/10216/110430
url https://hdl.handle.net/10216/110430
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1560-3547
10.1134/s1560354718030012
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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