Analytic reducibility of resonant cocycles to a normal form

Claire Chavaudret (1) , Laurent Stolovitch (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Systèmes dynamiques [math.DS]

Claire Chavaudret, Laurent Stolovitch. Analytic reducibility of resonant cocycles to a normal form. Journal of the Institute of Mathematics of Jussieu, 2016, 15 (1), pp.20. ⟨10.1017/S1474748014000383⟩. ⟨hal-01082651⟩