Analytic reducibility of resonant cocycles to a normal form

Abstract : We consider systems of quasi periodic linear differential equations associated to a 'resonant' frequency vector ω, that is a vector whose coordinates are not linearly independent over Z. We give sufficient conditions that ensure that a small analytic perturbation of a constant system is analytically conjugate to a 'resonant cocycle'. We also apply our results to the non resonant case : we obtain sufficient conditions for reducibility.
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Claire Chavaudret, Laurent Stolovitch. Analytic reducibility of resonant cocycles to a normal form. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2016, 15 (1), pp.20. ⟨10.1017/S1474748014000383 ⟩. ⟨hal-01082651⟩

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