Slow divergence integrals in generalized Liénard equations near centers

Abstract

Using techniques from singular perturbations we show that for any n≥6 and m≥2 there are Liénard 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 [⋅] denotes "the greatest integer equal or below".