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Invariant manifolds in singular perturbation problems for ordinary differential equations

Published online by Cambridge University Press:  14 November 2011

Kunimochi Sakamoto
Kunimochi Sakamoto
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, U.S.A.
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Synopsis

Based on Fenichel's geometric idea, invariant manifold theory is applied to singular perturbation problems. This approach clarifies the nature of outer and inner solutions. A specific condition is given to ensure the existence of heteroclinic connections between normally hyperbolic invariant manifolds. A method to approximate the connections is also presented.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 45 - 78
Copyright
Copyright © Royal Society of Edinburgh 1990

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