Regular Article
An Algebraic Approach to the Classification of Centers in Polynomial Liénard Systems

https://doi.org/10.1006/jmaa.1998.6175Get rights and content
Under an Elsevier user license
open archive

Abstract

We consider the second-order Liénard systemẍ+f(x)ẋ+g(x)=0,wheref(x) andg(x) are polynomials, which we rewrite in the equivalent two-dimensional form,ẋ=y,ẏ=−g(x)yf(x).We show that the local question of whether a critical point of this system is a center can be expressed in terms of global conditions onfandg. Using these results, we give a simple classification of all such centers. We also address the problem of the coexistence of centers, foci, and limit cycles for these systems. Systems with degenerate centers are also considered.

Cited by (0)

Submitted by U. Kirchgraber