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

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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

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