Dias, João LopesGalvão, João Pedro2023-10-062023-10-062019Dias, 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).0022-0396http://hdl.handle.net/10400.5/28897We 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.engGevrey FlowsGevrey TopologyDiophantine ConditionBrjuno Type VectorsArithmetical Conditionjournal articledoi.org/10.1016/j.jde.2019.07.020