1205.2070 (Ludwig Gauckler et al.)

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

Ludwig Gauckler, Ernst Hairer, Christian Lubich

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.

View original: http://arxiv.org/abs/1205.2070