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

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L. Gauckler, E. Hairer and C. Lubich

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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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Key Words. Hamiltonian systems, high oscillations, energy separation.

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