Géométrie, Algèbre, Dynamique et Topologie

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

## by Jean-Pierre FRANCOISE (Paris VI)

Europe/Paris
Salle 318 (IMB)

### Salle 318

#### IMB

Description

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.