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

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.

13 pages

References in corpus (2)

• Energy Transport in Weakly Anharmonic Chains
• Energy transfer in a fast-slow Hamiltonian system

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