Renormalisation of flows on the multidimensional torus close to a KT frequency vector

Detalhes bibliográficos
Autor(a) principal: Lopes, João Dias
Data de Publicação: 2002
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/29050
Resumo: We use a renormalisation operator R acting on a space of vector fields on t ᵈ , d ≥ 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point ω of R which is hyperbolic. This is done for a certain class KTd of frequency vectors ω ∈ R ᵈ , called of Koch type. The transformation R is constructed using a time rescaling, a linear change of basis plus a periodic non-linear map isotopic to the identity, which we derive by a “homotopy trick”.
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spelling Renormalisation of flows on the multidimensional torus close to a KT frequency vectorKAM TheoryReorganization GroupHamiltonian DynamicsWe use a renormalisation operator R acting on a space of vector fields on t ᵈ , d ≥ 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point ω of R which is hyperbolic. This is done for a certain class KTd of frequency vectors ω ∈ R ᵈ , called of Koch type. The transformation R is constructed using a time rescaling, a linear change of basis plus a periodic non-linear map isotopic to the identity, which we derive by a “homotopy trick”.Institute of Physics PublishingRepositório da Universidade de LisboaLopes, João Dias2023-10-16T10:21:25Z20022002-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29050engDias, João Lopes .(2002). “Renormalisation of flows on the multidimensional torus close to a KT frequency vector”. Nonlinearity Vol, 15,: pp. 647-664. (Search PDF in 2023).metadata 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:RCAAP2023-12-03T01:30:56Zoai:www.repository.utl.pt:10400.5/29050Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:39:19.851018Repositório 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 Renormalisation of flows on the multidimensional torus close to a KT frequency vector
title Renormalisation of flows on the multidimensional torus close to a KT frequency vector
spellingShingle Renormalisation of flows on the multidimensional torus close to a KT frequency vector
Lopes, João Dias
KAM Theory
Reorganization Group
Hamiltonian Dynamics
title_short Renormalisation of flows on the multidimensional torus close to a KT frequency vector
title_full Renormalisation of flows on the multidimensional torus close to a KT frequency vector
title_fullStr Renormalisation of flows on the multidimensional torus close to a KT frequency vector
title_full_unstemmed Renormalisation of flows on the multidimensional torus close to a KT frequency vector
title_sort Renormalisation of flows on the multidimensional torus close to a KT frequency vector
author Lopes, João Dias
author_facet Lopes, João Dias
author_role author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Lopes, João Dias
dc.subject.por.fl_str_mv KAM Theory
Reorganization Group
Hamiltonian Dynamics
topic KAM Theory
Reorganization Group
Hamiltonian Dynamics
description We use a renormalisation operator R acting on a space of vector fields on t ᵈ , d ≥ 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point ω of R which is hyperbolic. This is done for a certain class KTd of frequency vectors ω ∈ R ᵈ , called of Koch type. The transformation R is constructed using a time rescaling, a linear change of basis plus a periodic non-linear map isotopic to the identity, which we derive by a “homotopy trick”.
publishDate 2002
dc.date.none.fl_str_mv 2002
2002-01-01T00:00:00Z
2023-10-16T10:21:25Z
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/10400.5/29050
url http://hdl.handle.net/10400.5/29050
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Dias, João Lopes .(2002). “Renormalisation of flows on the multidimensional torus close to a KT frequency vector”. Nonlinearity Vol, 15,: pp. 647-664. (Search PDF in 2023).
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dc.publisher.none.fl_str_mv Institute of Physics Publishing
publisher.none.fl_str_mv Institute of Physics Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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