Abstract:

It is already known that the van der Pol limit cycle is not algebraic. Motivated for giving a simple proof of this fact we introduce some techniques to face this question. The newest one consists in simplifying as much as possible, and a priori, the cofactors of the possible invariant algebraic curves.

This is achieved using some birrational transformations, the so-called monomial maps. The tools introduced can be applied to study invariant algebraic hypersurfaces for general polynomial differential equations.

This talk is based on a joint work with A. Ferragut not yet finished. The talk will be in Catalan.