Abstract:

In 1977 Lins Neto, de Melo and Pugh [Lectures Notes in Math. 597, 335-357] conjectured that the classical Liénard system $x'=y-F(x), y'= -x, $ with $F(x)$ a real polynomial of degree $n$, has at most $[(n-1)/2]$ limit cycles, where $[ . ]$ denotes the integer part function. In this talk we summarize what is known and what is still open on this conjecture.

This talk is based in a joint paper with Xiang Zhang.