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Shooting methods and topological transversality

Published online by Cambridge University Press:  14 November 2011

B. Buffoni
B. Buffoni
Affiliation:
Département de mathématiques, Ecole Polytechnique Fédérate de Lausanne, 1015 Lausanne, Switzerland (Boris.Buffoni@epfl.ch)
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Extract

We show that shooting methods for homoclinic or heteroclinic orbits in dynamical systems may automatically guarantee the topological transversality of the stable and unstable manifolds. The interest of such results is twofold. First, these orbits persist under perturbations which destroy the structure allowing the shooting method and, second, topological transversality is often sufficient when some kind of transversality is required to obtain chaotic dynamics. We shall focus on heteroclinic solutions in the extended Fisher–Kolmogorov equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 6 , 1999 , pp. 1137 - 1155
Copyright
Copyright © Royal Society of Edinburgh 1999

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