Abstract

This is a recent work with Jaume Llibre. We prove that any classical Liénard equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins,W. de Melo and C.C. Pugh in 1977 about the number of limit cycles for polynomial Liénard equations for n=4.

We continue on the previous talk with the same title.

In the previous talk I first introduced the background of the problem, then talked about how to transform the equations to a good form, and how to study the divergence integral in some cases, in order to prove the main result. In this talk I will focus on the study of the divergence integral in the remaining cases.