Normal forms of topologically quasi-homogeneous foliations on $({\text{C}}^2,0)$

The aim of this paper is to construct formal normal forms for the class of topologically quasi-homogeneous foliations under generic conditions. Any such normal form is given as the sum of three terms: an initial generic quasi-homogeneous term, a hamiltonian term and a radial term. Moreover, we also show that the number of free coefficients in the hamiltonian part is consistent with the dimension of Mattei’s moduli space of unfoldings.