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

2019Journal article Open access
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dc.contributor.authorDias, João Lopes
dc.contributor.authorGalvão, João Pedro
dc.date.accessioned2023-10-06T09:09:37Z
dc.date.available2023-10-06T09:09:37Z
dc.date.issued2019
dc.description.abstractWe 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationDias, 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).pt_PT
dc.identifier.doidoi.org/10.1016/j.jde.2019.07.020pt_PT
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10400.5/28897
dc.language.isoengpt_PT
dc.publisherElsevierpt_PT
dc.subjectGevrey Flowspt_PT
dc.subjectGevrey Topologypt_PT
dc.subjectDiophantine Conditionpt_PT
dc.subjectBrjuno Type Vectorspt_PT
dc.subjectArithmetical Conditionpt_PT
dc.titleLinearization of Gevrey flows on T ͩ with a Brjuno type arithmetical conditionpt_PT
dc.typejournal article
dspace.entity.typePublication
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT

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