Asymptotic expansions using blow-up


Gils, S. van and Krupa, M. and Szmolyan, P. (2005) Asymptotic expansions using blow-up. Zeitschrift für Angewandte Mathematik und Physik, 56 (3). pp. 369-397. ISSN 0044-2275

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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.
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Copyright:© 2005 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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