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Normal form of perturbations of quasihomogeneous vector fields. (Forme normale de perturbation de champs de vecteurs quasi-homogènes.) (French) Zbl 1161.37037
The authors consider holomorphic vector fields in a neighbourhood of the origin of \({\mathbb C}^n\) which are suitable perturbations of a quasihomogeneous vector field. (Hence the origin is its fixed point.) They define a “diophantine condition” on the quasihomogeneous initial part \(S\) of the vector field which ensures that if such a perturbation is formally conjugate to \(S\), then it is also holomorphically conjugate to it.

MSC:
37G05 Normal forms for dynamical systems
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