Fulltext

Results on Normal Forms for FPU Chains

Henrici, Andreas ; Kappeler, Thomas

In: Communications in Mathematical Physics, 2008, vol. 278, no. 1, p. 145-177

Add to personal list
    Title
    • Results on Normal Forms for FPU Chains
    Author
    • Henrici, Andreas. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
    • Kappeler, Thomas. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Communications in Mathematical Physics, 2008, vol. 278, no. 1, p. 145-177. Springer-Verlag
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:315813
    Summary
    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