Compactification and desingularization of spaces of polynomial Lienard equations

Abstract

The paper deals with polynomial Lienard equations of type (m, n), i.e. planar vector fields associated to a scalar second order differential equation x + f (x)x + g(x) = 0, with f and g polynomials of respective degree m and n. It is shown that, besides compactifying the phase plane, or the Lienard plane, one can also compactify and desingularize the space of Lienard equations of type (m, n) for each (m, n) separately, by adding both singular perturbation problems and Hamiltonian perturbation problems. (c) 2005 Elsevier Inc. All rights reserved.