Time and entry-exit relation near a planar turning point

Abstract

Following the geometric approach for studying singular perturbation problems in the plane at turning points, and considering a very general setting where canard solutions are shown to exist, we study the transition time of orbits passing near the turning point, as well as the entry-exit relation at such turning points. The manifolds of canard solutions are in general only C-0 at the turning point, making the classical asymptotic approach impossible. The method involves a (family) blow up of the turning point and the use of C-k -normal forms and center manifolds. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.