Normal form of perturbations of quasihomogeneous vector fields (Q1004542)

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.