Abstract :
We are interested in singularities of analytic vector fields in (real or complex) dimension 2, up to changes of coordinates and reparametrization of time. Two integers p,q * being fixed, we give a list of models for small perturbations of the Hamiltonian vector field X = pyp −1(∂/∂x) + qxq −1(∂/∂y) associated with the function H(x, y) = yp −xq. Each of these perturbations reduces by formal changes of coordinates to one and only one of our models, by an explicit algorithm. These perturbations are no more Hamiltonian. We derive by this way an uncountable dimensional space of distinct analytic classes of such perturbations. The Introduction ends with questions about problems of convergence
