A Shadowing Approach to Passage Through Resonance

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1990_Murdock_ShadowingApproach001.PDF (10.91 MB)
Date
1990
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Murdock, James
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Mathematics
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Abstract

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.
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This article is published as A Shadowing Approach to Passage Through Resonance, Proceedings of the Royal Society of Edinburgh 116A, 1990, 1-22 and also in New Directions in Differential Equations and Dynamical Systems, ed. J. M. Ball, Royal Society of Edinburgh, 1991. doi:10.1017/S0308210500031358. Posted with permission.

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http://doi.org/10.1017/S0308210500031358
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https://dr.lib.iastate.edu/handle/20.500.12876/54493
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Mathematics
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Mon Jan 01 00:00:00 UTC 1990
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