Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition

Detalhes bibliográficos
Autor(a) principal: Dias, João Lopes
Data de Publicação: 2019
Outros Autores: Galvão, João Pedro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/28897
Resumo: We show that in the Gevrey topology, a d-torus flow close enough to linear with a unique rotation vector ω is linearizable as long as ω satisfies a novel Brjuno type diophantine condition. The proof is based on the fast convergence under renormalization of the associated Gevrey vector field. It requires a multidimensional continued fractions expansion of ω, and the corresponding characterization of the Brjuno type vectors. This demonstrates that renormalization methods deal very naturally with Gevrey regularity expressed in the decay of Fourier coefficients. In particular, they provide new linearization results including frequencies beyond diophantine in non-analytic topologies.
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spelling Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical conditionGevrey FlowsGevrey TopologyDiophantine ConditionBrjuno Type VectorsArithmetical ConditionWe show that in the Gevrey topology, a d-torus flow close enough to linear with a unique rotation vector ω is linearizable as long as ω satisfies a novel Brjuno type diophantine condition. The proof is based on the fast convergence under renormalization of the associated Gevrey vector field. It requires a multidimensional continued fractions expansion of ω, and the corresponding characterization of the Brjuno type vectors. This demonstrates that renormalization methods deal very naturally with Gevrey regularity expressed in the decay of Fourier coefficients. In particular, they provide new linearization results including frequencies beyond diophantine in non-analytic topologies.ElsevierRepositório da Universidade de LisboaDias, João LopesGalvão, João Pedro2023-10-06T09:09:37Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28897engDias, João Lopes and João Pedro Galvão .(2019). “Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition”. Journal of Differential Equations, Volume 267, No. 12: pp. 7167-7212 . (Search PDF in 2023).0022-0396doi.org/10.1016/j.jde.2019.07.020info: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:RCAAP2023-10-22T01:31:59Zoai:www.repository.utl.pt:10400.5/28897Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:56.929934Repositório 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 Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
title Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
spellingShingle Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
Dias, João Lopes
Gevrey Flows
Gevrey Topology
Diophantine Condition
Brjuno Type Vectors
Arithmetical Condition
title_short Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
title_full Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
title_fullStr Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
title_full_unstemmed Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
title_sort Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
author Dias, João Lopes
author_facet Dias, João Lopes
Galvão, João Pedro
author_role author
author2 Galvão, João Pedro
author2_role author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Dias, João Lopes
Galvão, João Pedro
dc.subject.por.fl_str_mv Gevrey Flows
Gevrey Topology
Diophantine Condition
Brjuno Type Vectors
Arithmetical Condition
topic Gevrey Flows
Gevrey Topology
Diophantine Condition
Brjuno Type Vectors
Arithmetical Condition
description We show that in the Gevrey topology, a d-torus flow close enough to linear with a unique rotation vector ω is linearizable as long as ω satisfies a novel Brjuno type diophantine condition. The proof is based on the fast convergence under renormalization of the associated Gevrey vector field. It requires a multidimensional continued fractions expansion of ω, and the corresponding characterization of the Brjuno type vectors. This demonstrates that renormalization methods deal very naturally with Gevrey regularity expressed in the decay of Fourier coefficients. In particular, they provide new linearization results including frequencies beyond diophantine in non-analytic topologies.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
2023-10-06T09:09:37Z
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/10400.5/28897
url http://hdl.handle.net/10400.5/28897
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Dias, João Lopes and João Pedro Galvão .(2019). “Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition”. Journal of Differential Equations, Volume 267, No. 12: pp. 7167-7212 . (Search PDF in 2023).
0022-0396
doi.org/10.1016/j.jde.2019.07.020
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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