Extension aux cycles singuliers du theoreme de Khovanski-Varchenko

Abstract

Let dH be a Hamiltonian one form on the real plane, of degre d. We show that, if H is a Morse function, generic at infinity, then there exists a number N(d) depending only on d, such that every small perturbation of dH has at most N(d) limit cycles on the hole real plane, assuming that it's of degre at most d, and that it has a non vanishing Abelian integral along real cycles of dH.