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A shadowing approach to passage through resonance

Published online by Cambridge University Press:  14 November 2011

James A. Murdoch
James A. Murdoch
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
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Synopsis

Leading order approximations are given by a patching method for passage through resonance in the case when the resonance zone contains saddle points. The approximations are uniformly valid regardless of the length of time required to pass through the resonance. Accuracy for extended time periods is obtained by asking not for approximate solutions with specified initial values, but for approximate solutions which are “shadowed” by exact solutions in the resonance zone.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 1 - 22
Copyright
Copyright © Royal Society of Edinburgh 1990

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