Forme normale de perturbation de champs de vecteurs quasi-homogènes

Abstract: In this Note, we study germs of holomorphic vector fields which are suitable perturbations of a quasihomogeneous vector field in a neighborhood of the origin of , fixed point of the vector fields. In particular, we define a “diophantine condition” on the quasihomogeneous initial part S which ensures that if such a perturbation of S is formally conjugate to S then it is also holomorphically conjugate to it. To cite this article: E. Lombardi, L. Stolovitch, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]