Melnikov Functions and Bautin Ideal

摘要: The computation of the number limit cycles which appear in an analytic unfolding planar vector fields is related to decomposition displacement function this ideal functions parameter space, called Ideal Bautin. On other hand, asymptotic function, for 1-parameter unfoldings hamiltonian given by Melnikov are defined as coefficients Taylor expansion parameter. It interesting compare these two notions and study if general estimations terms Bautin could be reduced computations some subfamilies.