Asymptotic expansions using blowup

Asymptotic expansions using blowup

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 techn...

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Veröffentlicht in:Zeitschrift für angewandte Mathematik und Physik 2005-05, Vol.56 (3), p.369-397
Hauptverfasser: Van Gils, S, Krupa, M, Szmolyan, P
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creator Van Gils, S
Krupa, M
Szmolyan, P
description 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.
doi_str_mv 10.1007/s00033-004-1021-y
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title Asymptotic expansions using blowup
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