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Energy separation in oscillatory Hamiltonian systems without any non-resonance condition

Please always quote using this URN:urn:nbn:de:0296-matheon-11891
  • We consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary N>1, where eps^{-1} is the size of the smallest high frequency. The result is uniform in the frequencies and does not require non-resonance conditions.

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Metadaten
Author:Ludwig Gauckler, Ernst Hairer, Christian Lubich
URN:urn:nbn:de:0296-matheon-11891
Referee:Reinhold Schneider
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/11/06
Release Date:2013/11/06
Tag:multiscale Hamiltonian systems; oscillatory energy; resonances
Institute:Research Center Matheon
Technische Universität Berlin
MSC-Classification:70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Hxx Hamiltonian and Lagrangian mechanics [See also 37Jxx] / 70H05 Hamilton`s equations
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Kxx Nonlinear dynamics [See also 34Cxx, 37-XX] / 70K70 Systems with slow and fast motions
Preprint Number:1043
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