Gevrey properties of real planar singularly perturbed systems

By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of center manifolds at normally hyperbolic turning points, and show that the same technique is useful in the study of degenerate planar turning points and their corresponding canard manifolds. At the end of the Note, we motivate the interest in Gevrey asymptotics by briefly discussing its relation with bifurcation delay. To cite this article: P. De Maesschalck, C. R. Acad. Sci. Paris, Ser. I 340 (2005).