# Hilbert's 16th problem on a period annulus and Nash space of arcs

Date:
22.05.18
Times:
12:00 to 13:00
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Jean-Pierre Françoise
University:
Université de Pierre et Marie Curie

#### Abstract:

This is a joint article with Lubomir Gavrilov and Dongmei Xiao.
We use the Nash Space of arcs of the blow-up of the Bautin ideal and show the identification of points on the exceptional divisor with the bifurcations functions. This geometrical setting allows to define more precisely the essential perturbations in the sense of Iliev. In particular, we discuss the case of quadratic vector fields of the plane.
Several open questions are solved using finiteness of some Iliev numbers shown within this geometrical setting.