Systeme des coordonees plates de la deformation verselle des singularites isolees simples d'hypersurface et zeros de l'integrale d'Abel

Abstract

One studies a system of differential equations defined by Abel integrals associated to a real cycle defined for the versal deformation of an isolated simple singularity. As application, one obtains an estimation on the multiplicity of zeros of the Abel integral in terms of quasihomogeneous weights associated to the Hamiltonian and the integrand function.