Sharp upperbounds for the number of large amplitude limit cycles in polynomial Lienard systems

Abstract

In [1] and [2] upperbounds have been given for the number of large amplitude limit cycles in polynomial Liénard systems of type $(m,n)$ with $m<2n+1$, $m$ and $n$ odd. In the current paper we improve the upperbounds from [1] and [2] by one unity, obtaining sharp results. We therefore introduce the 'method of cloning variables' that might be useful in other cyclicity problems.