Generic dynamics of 4-dimensional C² Hamiltonian systems

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2008
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/10400.5/28971
Resumo: We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].
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spelling Generic dynamics of 4-dimensional C² Hamiltonian systemsHamiltonian SystemsGeneric DynamicsProbabilistic PerspectiveWe study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].SpringerRepositório da Universidade de LisboaBessa, MárioDias, João Lopes2023-10-13T09:26:04Z20082008-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28971engBessa, Mário and João Lopes Dias .(2008). “Generic dynamics of 4-dimensional C² Hamiltonian systems”. Communications in Mathematical Physics, Volume 281: pp. 597–619. (Search PDF in 2023).1432-0916info: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:RCAAP2023-10-15T01:33:48Zoai:www.repository.utl.pt:10400.5/28971Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:35:46.276975Repositório 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 Generic dynamics of 4-dimensional C² Hamiltonian systems
title Generic dynamics of 4-dimensional C² Hamiltonian systems
spellingShingle Generic dynamics of 4-dimensional C² Hamiltonian systems
Bessa, Mário
Hamiltonian Systems
Generic Dynamics
Probabilistic Perspective
title_short Generic dynamics of 4-dimensional C² Hamiltonian systems
title_full Generic dynamics of 4-dimensional C² Hamiltonian systems
title_fullStr Generic dynamics of 4-dimensional C² Hamiltonian systems
title_full_unstemmed Generic dynamics of 4-dimensional C² Hamiltonian systems
title_sort Generic dynamics of 4-dimensional C² Hamiltonian systems
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 Systems
Generic Dynamics
Probabilistic Perspective
topic Hamiltonian Systems
Generic Dynamics
Probabilistic Perspective
description We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-01-01T00:00:00Z
2023-10-13T09:26:04Z
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/10400.5/28971
url http://hdl.handle.net/10400.5/28971
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, Mário and João Lopes Dias .(2008). “Generic dynamics of 4-dimensional C² Hamiltonian systems”. Communications in Mathematical Physics, Volume 281: pp. 597–619. (Search PDF in 2023).
1432-0916
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 Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron_str RCAAP
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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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