Thursday, May 10, 2012

1205.2070 (Ludwig Gauckler et al.)

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

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.
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