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Hamiltonian Systems

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Averaging Methods in Nonlinear Dynamical Systems

Part of the book series: Applied Mathematical Sciences ((AMS,volume 59))

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Abstract

In Hamiltonian mechanics, the small parameter necessary to do asymptotics is usually obtained by localizing the system around some wellknown solution, e.g. an equilibrium. As we shall see, the part played by the small parameter in the normal form of the Hamiltonian determines the asymptotic estimates which we can obtain. In the various resonance cases which we shall discuss, these estimates take different forms the theory of which is based on the preceding chapters with special extensions for the Hamiltonian context.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Free University, 1007 MA, Amsterdam, The Netherlands

    Jan A. Sanders

  2. Mathematical Institute, State University of Utrecht, 3508 TA, Utrecht, The Netherlands

    Ferdinand Verhulst

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  1. Jan A. Sanders
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  2. Ferdinand Verhulst
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Sanders, J.A., Verhulst, F. (1985). Hamiltonian Systems. In: Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4575-7_7

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  • DOI: https://doi.org/10.1007/978-1-4757-4575-7_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96229-0

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