Hamiltonian suspension of perturbed Poincaré sections and an application

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2014
Outros Autores: Dias, João Lopes
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/28902
Resumo: We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any point p ∈ M, there exists a C ² -close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency.
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spelling Hamiltonian suspension of perturbed Poincaré sections and an applicationHamiltonian Vector FieldAnosov FlowElliptic PointHomoclinic TangencyWe construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any point p ∈ M, there exists a C ² -close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency.Cambridge University PressRepositório da Universidade de LisboaBessa, MárioDias, João Lopes2023-10-06T15:03:36Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28902engBessa, Mário and João Lopes Dias .(2014). “ Hamiltonian suspension of perturbed Poincaré sections and an application”. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 157: pp. 101-1121469-8064metadata only accessinfo: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:RCAAP2023-10-08T01:32:21Zoai:www.repository.utl.pt:10400.5/28902Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:57.257248Repositório 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 Hamiltonian suspension of perturbed Poincaré sections and an application
title Hamiltonian suspension of perturbed Poincaré sections and an application
spellingShingle Hamiltonian suspension of perturbed Poincaré sections and an application
Bessa, Mário
Hamiltonian Vector Field
Anosov Flow
Elliptic Point
Homoclinic Tangency
title_short Hamiltonian suspension of perturbed Poincaré sections and an application
title_full Hamiltonian suspension of perturbed Poincaré sections and an application
title_fullStr Hamiltonian suspension of perturbed Poincaré sections and an application
title_full_unstemmed Hamiltonian suspension of perturbed Poincaré sections and an application
title_sort Hamiltonian suspension of perturbed Poincaré sections and an application
author Bessa, Mário
author_facet Bessa, Mário
Dias, João Lopes
author_role author
author2 Dias, João Lopes
author2_role author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Bessa, Mário
Dias, João Lopes
dc.subject.por.fl_str_mv Hamiltonian Vector Field
Anosov Flow
Elliptic Point
Homoclinic Tangency
topic Hamiltonian Vector Field
Anosov Flow
Elliptic Point
Homoclinic Tangency
description We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any point p ∈ M, there exists a C ² -close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2023-10-06T15:03:36Z
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://hdl.handle.net/10400.5/28902
url http://hdl.handle.net/10400.5/28902
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, Mário and João Lopes Dias .(2014). “ Hamiltonian suspension of perturbed Poincaré sections and an application”. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 157: pp. 101-112
1469-8064
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
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