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. To cite this article: P. De Maesschalck, F. Dumortier, C. R. Acad. Sci. Paris, Ser. I 339 (2004).
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