The infinitesimal 16th Hilbert problem in the quadratic case

Let H(x, y) be a real cubic polynomial with four distinct critical values (in a complex domain) and let X-H = H-y partial derivative/partial derivativex - H-x partial derivative/partial derivativey be the corresponding Hamiltonian vector field. We show that there is a neighborhood U of X-H in the space of all quadratic plane vector fields, such that any X epsilon U has at most two limit cycles.