Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 33, Issue 2, Pages 286-314Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036141099360919
Keywords
singular perturbations; slow manifolds; nonhyperbolicity; blow-up; folds; canards
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The geometric approach to singular perturbation problems is based on powerful methods from dynamical systems theory. These techniques have been very successful in the case of normally hyperbolic critical manifolds. However, at points where normal hyperbolicity fails, the well-developed geometric theory does not apply. We present a method based on blow-up techniques, which leads to a rigorous geometric analysis of these problems. A detailed analysis of the extension of slow manifolds past fold points and canard points in planar systems is given. The efficient use of various charts is emphasized.
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