Slow divergence integrals in generalized Lienard equations near centers

Abstract

Using techniques from singular perturbations we show that for any n >= 6 and m >= 2 there are Lienard equations {x = y - F(x), y = G ( x)}, with F a polynomial of degree n and G a polynomial of degree m, having at least 2[n-2/2] + [m/2] hyperbolic limit cycles, where [center dot] denotes "the greatest integer equal or below".