Energy separation in oscillatory Hamiltonian systems without any non-resonance condition
Dynamical Systems
2015-06-05 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
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.
Keywords
Cite
@article{arxiv.1205.2070,
title = {Energy separation in oscillatory Hamiltonian systems without any non-resonance condition},
author = {Ludwig Gauckler and Ernst Hairer and Christian Lubich},
journal= {arXiv preprint arXiv:1205.2070},
year = {2015}
}
Comments
13 pages