Publicação
Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition
| 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. |
|---|---|
| Autores principais: | Dias, João Lopes |
| Outros Autores: | Galvão, João Pedro |
| Assunto: | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866809781011873792 |
|---|---|
| author | Dias, João Lopes |
| author2 | Galvão, João Pedro |
| author2_role | author |
| author_facet | Dias, João Lopes Galvão, João Pedro |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Dias, João Lopes\"},{\"Person.name\":\"Galvão, João Pedro\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Dias, João Lopes Galvão, João Pedro |
| datacite.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-10-06T09:09:37Z |
| datacite.date.embargoed.fl_str_mv | 2023-10-06T09:09:37Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| datacite.titles.title.fl_str_mv | Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Dias, João Lopes Galvão, João Pedro |
| dc.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-10-06T09:09:37Z |
| dc.date.embargoed.fl_str_mv | 2023-10-06T09:09:37Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/28897 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| dc.title.fl_str_mv | Linearization of Gevrey flows on T ͩ with a Brjuno type arithmetical condition |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/982f3cbd-6105-48a3-b386-ceacf87e1ecc/download |
| id | ul_bb4fb0b4b2d80a0f8606342d27dfa67b |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/28897 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/28897 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Dias, João Lopes Galvão, João Pedro |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Elsevier |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engElsevierpt_PTWe 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.application/pdfpt_PTLinearization of Gevrey flows on T ͩ with a Brjuno type arithmetical conditionDias, João LopesGalvão, João PedroHostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISSNIsPartOf0022-0396DOIIsPartOfdoi.org/10.1016/j.jde.2019.07.0202023-10-06T09:09:37Z20192019-01-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/28897http://purl.org/coar/access_right/c_abf2open accessGevrey FlowsGevrey TopologyDiophantine ConditionBrjuno Type VectorsArithmetical Condition502689 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/982f3cbd-6105-48a3-b386-ceacf87e1ecc/download |
| 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 |
| status | SINGLETON |
| subject.fl_str_mv | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| title | 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_short | 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 |
| topic | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| topic_facet | Gevrey Flows Gevrey Topology Diophantine Condition Brjuno Type Vectors Arithmetical Condition |
| url | http://hdl.handle.net/10400.5/28897 |
| visible | 1 |