Energy separation in oscillatory Hamiltonian systems without any   non-resonance condition
  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. 
Ludwig Gauckler, Ernst Hairer, Christian Lubich
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