Compactification and desingularization of spaces of polynomial Liénard equations

The paper deals with polynomial Liénard equations of type (m,n), i.e. planar vector fields associated to a scalar second order differential equation , with f and g polynomials of respective degree m and n. It is shown that, besides compactifying the phase plane, or the Liénard plane, one can also compactify and desingularize the space of Liénard equations of type (m,n) for each (m,n) separately, by adding both singular perturbation problems and Hamiltonian perturbation problems.