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Long-Time Accuracy for Approximate Slow Manifolds in a Finite-Dimensional Model of Balance | Journal of Nonlinear Science Skip to main content
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Long-Time Accuracy for Approximate Slow Manifolds in a Finite-Dimensional Model of Balance

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Abstract

We study the slow singular limit for planar anharmonic oscillatory motion of a charged particle under the influence of a perpendicular magnetic field when the mass of the particle goes to zero. This model has been used by the authors as a toy model for exploring variational high-order approximations to the slow dynamics in rotating fluids. In this paper, we address the long time validity of the slow limit equations in the simplest nontrivial case. We show that the first-order reduced model remains O(ε) accurate over a long 1/ε timescale. The proof is elementary, but involves subtle estimates on the nonautonomous linearized dynamics.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia

    G. Gottwald

  2. School of Engineering and Science, Jacobs University Bremen, 28759 Bremen, Germany

    M. Oliver

  3. Department of Mathematics, Yale University, New Haven, CT 06520, USA

    N. Tecu

Authors
  1. G. Gottwald
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  2. M. Oliver
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  3. N. Tecu
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Corresponding authors

Correspondence to G. Gottwald, M. Oliver or N. Tecu.

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Gottwald, G., Oliver, M. & Tecu, N. Long-Time Accuracy for Approximate Slow Manifolds in a Finite-Dimensional Model of Balance. J Nonlinear Sci 17, 283–307 (2007). https://doi.org/10.1007/s00332-006-0804-2

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  • DOI: https://doi.org/10.1007/s00332-006-0804-2

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