Asymptotic expansions using blow-up |
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Authors: | S. van Gils M. Krupa P. Szmolyan |
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Affiliation: | (1) Faculteit Toegepaste Wiskunde, Technische Universiteit Twente, Enschede, The Netherelands;(2) Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstraße 8–10, A-1040 Wien, Austria |
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Abstract: | The method of matched asymptotic expansions and geometric singular perturbation theory are the most common and successful approaches to singular perturbation problems. In this work we establish a connection between the two approaches in the context of the simple fold problem. Using the blow-up technique [5], [12] and the tools of geometric singular perturbation theory we derive asymptotic expansions of slow manifolds continued beyond the fold point. Our analysis explains the structure of the expansion and gives an algorithm for computing its coefficients.*Research supported by the Austrian Science Foundation under grant Y 42-MAT.Received: February 1, 2001; revised: November 22, 2002 |
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Keywords: | 37D10 34B15 |
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