TY - GEN A1 - Gauckler, Ludwig A1 - Hairer, Ernst A1 - Lubich, Christian T1 - Energy separation in oscillatory Hamiltonian systems without any non-resonance condition N2 - 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. KW - multiscale Hamiltonian systems KW - oscillatory energy KW - resonances Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1189 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11891 ER -