Hamiltonian elliptic dynamics on symplectic 4-manifolds

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2009
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/10400.5/28970
Resumo: We consider C²-Hamiltonian functions on compact 4-dimensional symplectic manifolds to study the elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that, for far from Anosov regular energy surfaces of a C²-generic Hamiltonian, the elliptic closed orbits are generic.
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spelling Hamiltonian elliptic dynamics on symplectic 4-manifoldsHamiltonian FunctionsElliptic DynamicsGeometric and Probabilistic PerspectiveWe consider C²-Hamiltonian functions on compact 4-dimensional symplectic manifolds to study the elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that, for far from Anosov regular energy surfaces of a C²-generic Hamiltonian, the elliptic closed orbits are generic.American Mathematical Society (AMS)Repositório da Universidade de LisboaBessa, MárioDias, João Lopes2023-10-13T08:26:50Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28970engBessa, Mário and João Lopes Dias .(2009). “Hamiltonian elliptic dynamics on symplectic 4-manifolds” . Proceedings American Mathematical Society, Volume 137, Number 2: pp. 585–592 (Search PDF in 2023).1088-6826info: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:RCAAP2023-10-15T01:33:47Zoai:www.repository.utl.pt:10400.5/28970Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:35:46.188772Repositório 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 elliptic dynamics on symplectic 4-manifolds
title Hamiltonian elliptic dynamics on symplectic 4-manifolds
spellingShingle Hamiltonian elliptic dynamics on symplectic 4-manifolds
Bessa, Mário
Hamiltonian Functions
Elliptic Dynamics
Geometric and Probabilistic Perspective
title_short Hamiltonian elliptic dynamics on symplectic 4-manifolds
title_full Hamiltonian elliptic dynamics on symplectic 4-manifolds
title_fullStr Hamiltonian elliptic dynamics on symplectic 4-manifolds
title_full_unstemmed Hamiltonian elliptic dynamics on symplectic 4-manifolds
title_sort Hamiltonian elliptic dynamics on symplectic 4-manifolds
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 Functions
Elliptic Dynamics
Geometric and Probabilistic Perspective
topic Hamiltonian Functions
Elliptic Dynamics
Geometric and Probabilistic Perspective
description We consider C²-Hamiltonian functions on compact 4-dimensional symplectic manifolds to study the elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that, for far from Anosov regular energy surfaces of a C²-generic Hamiltonian, the elliptic closed orbits are generic.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01T00:00:00Z
2023-10-13T08:26:50Z
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://hdl.handle.net/10400.5/28970
url http://hdl.handle.net/10400.5/28970
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, Mário and João Lopes Dias .(2009). “Hamiltonian elliptic dynamics on symplectic 4-manifolds” . Proceedings American Mathematical Society, Volume 137, Number 2: pp. 585–592 (Search PDF in 2023).
1088-6826
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.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
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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