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Abstract: In this paper we investigate periodic FPU chains with an even number ofparticles. We show that near the equilibrium point, any such chain admits a\emph{resonant} Birkhoff normal form of order four which is \emph{completelyintegrable} - an important fact which helps explain the numerical experimentsof Fermi, Pasta, and Ulam. We analyze the moment map of the integrableapproximation of an even FPU chain. Unlike in the case of odd FPU chains theseintegrable systems generically exhibit hyperbolic dynamics. As an applicationwe prove that any FPU chain with Dirichlet boundary conditions admits aBirkhoff normal form up to order four and show that a KAM theorem applies.



Author: Andreas Henrici, Thomas Kappeler

Source: https://arxiv.org/



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