Bifurcations de cycles limites, problème du centre et espace des arcs de Nash

par Jean-Pierre FRANCOISE (Paris VI)

jeudi 3 oct. 2019, 10:30 → 12:00 Europe/Paris

Salle 318 (IMB)

This article introduces an algebro-geometric setting for the space of bifurcation functions involved in the local Hilbert's 16th problem on a period annulus. Each possible bifurcation function is in one-to-one correspondence with a point in the exceptional divisor $E$ of the canonical blow-up $B_I{\mathbb{C}}^n$ of the Bautin ideal $I$. In this setting, the notion of essential perturbation, first proposed by Iliev, is defined via irreducible components of the Nash space of arcs $Arc(B_I{\mathbb{C}}^n,E)$. The example of planar quadratic vector fields in the Kapteyn normal form is further discussed.