2007/09/17 by Andreas Henrici, Henrici, Andreas, Thomas Kappeler +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS #nlin.SI
paper · pdf · doi:10.48550/arxiv.0709.2624
34 pages, 3 figures
arxiv created 2007/09/17 · openalex publication_date 2007/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper 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 in 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.