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

Dynamical Systems 2015-06-05 v2 Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

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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Cite

@article{arxiv.1205.2070,
  title  = {Energy separation in oscillatory Hamiltonian systems without any non-resonance condition},
  author = {Ludwig Gauckler and Ernst Hairer and Christian Lubich},
  journal= {arXiv preprint arXiv:1205.2070},
  year   = {2015}
}

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13 pages