Geodesic
Resonant normal form for even periodic FPU chains
Journal of the European Mathematical Society, Tome 11 (2009) no. 5, pp. 1025-1056 Cet article a éte moissonné depuis la source EMS Press

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We investigate periodic FPU chains with an even number of particles. We show that near the equilibrium point, any such chain admits a resonant Birkhoff normal form of order four which is completely integrable—an important fact which helps explain the numerical experiments of Fermi, Pasta, and Ulam. We analyze the moment map of the integrable approximation of an even FPU chain. Unlike the case of odd FPU chains these integrable systems (generically) exhibit hyperbolic dynamics. As an application we prove that any FPU chain with Dirichlet boundary conditions admits a Birkhoff normal form up to order four and show that a KAM theorem applies.
DOI : 10.4171/jems/174
Classification : 35-XX, 00-XX 
@article{JEMS_2009_11_5_a3,
     author = {Andreas Henrici and Thomas Kappeler},
     title = {Resonant normal form for even periodic {FPU} chains},
     journal = {Journal of the European Mathematical Society},
     pages = {1025--1056},
     year = {2009},
     volume = {11},
     number = {5},
     doi = {10.4171/jems/174},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/174/}
}
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Andreas Henrici; Thomas Kappeler. Resonant normal form for even periodic FPU chains. Journal of the European Mathematical Society, Tome 11 (2009) no. 5, pp. 1025-1056. doi: 10.4171/jems/174

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