Energy separation in oscillatory Hamiltonian systems without any non-resonance condition
Please always quote using this URN:urn:nbn:de:0296-matheon-11891
- 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.
Author: | Ludwig Gauckler, Ernst Hairer, Christian Lubich |
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URN: | urn:nbn:de:0296-matheon-11891 |
Referee: | Reinhold Schneider |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2013/11/06 |
Release Date: | 2013/11/06 |
Tag: | multiscale Hamiltonian systems; oscillatory energy; resonances |
Institute: | Research Center Matheon |
Technische Universität Berlin | |
MSC-Classification: | 70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Hxx Hamiltonian and Lagrangian mechanics [See also 37Jxx] / 70H05 Hamilton`s equations |
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Kxx Nonlinear dynamics [See also 34Cxx, 37-XX] / 70K70 Systems with slow and fast motions | |
Preprint Number: | 1043 |