| 概要 | We study germs of holomorphic vector fields which are
"higher order" perturbations of a quasihomogeneous vector
field in a neighborhood of the origin of C^n, fixed point
of the vector fields. 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. We study
the normal form problem relatively to S. We give a condition
on S that ensure that there always exists an holomorphic
transformation to a normal form. If this condition is not
satisfied, we also show, that under some reasonable
assumptions, each perturbation of S admits a Gevrey formal
normalizing transformation.
|