Abstract
In this paper we prove, among other results, that near the equilibirum position, any periodic FPU chain with an odd number N of particles admits a Birkhoff normal form up to order 4, whereas any periodic FPU chain with N even admits a resonant normal form up to order 4. This resonant normal form of order 4 turns out to be completely integrable. Further, for N odd, we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.
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Communicated by G. Gallavotti
Supported in part by the Swiss National Science Foundation.
Supported in part by the Swiss National Science Foundation, the programme SPECT and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652).
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Henrici, A., Kappeler, T. Results on Normal Forms for FPU Chains. Commun. Math. Phys. 278, 145–177 (2008). https://doi.org/10.1007/s00220-007-0387-z
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DOI: https://doi.org/10.1007/s00220-007-0387-z