Gevrey asymptotics of singularly perturbed vector fields in the blowup space
by
Peter De Maesschalck
Departement WNI, Limburgs Universitair Centrum , B-3590 Diepenbeek

In the context of singular perturbations (with 1 slow variable) we examine the properties of center manifolds existing along the slow curve. More specifically, we look at the the coefficient growth of the asymptotic expansion of these manifolds. It is a known result (Sibuya) that this growth is of Gevrey-type in the neighbourhood of normally hyperbolic singular points. We extend these results in a way to points where normal hyperbolicity is lost, by blowing up up that point and studying the situation most likely to encounter after blowup. The difficulty in proving the Gevrey asymptotics lies in the fact that the trivial foliation d\epsilon = 0 along which we normally expand is replaced with a foliation of the kind (du^pv^q)=0.

Date received: April 30, 2001