Gevrey properties of real planar singularly perturbed systems |
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Authors: | P De Maesschalck |
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Institution: | Hasselt University, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium |
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Abstract: | 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 canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions. |
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Keywords: | Singular perturbations Canard solution Overstable solution Gevrey asymptotics Degenerate turning point Family blow up |
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