Improving a method for the study of limit cycles of the Liénard equation
Résumé
In recent papers we have introduced a method for the study of limit cycles of the Liénard system, $\dot x=y-F(x)$, $\dot y=-x$, where $F(x)$ is an odd polynomial. The method gives a sequence of polynomials $R_n(x)$, whose roots are related to the number and location of the limit cycles, and a sequence of algebraic approximations to the bifurcation set of the system. In this paper, we present a variant of the method that gives very important qualitative and quantitative improvements.