Near-integrability of periodic FPU-chains

Bob Rink and Ferdinand Verhulst

Physica A: Statistical Mechanics and its Applications, 2000, vol. 285, issue 3, 467-482

Abstract: The FPU-chain with periodic boundary conditions is studied by Birkhoff–Gustavson normalisation. In the cases of up to 6 particles and for β-chains with an odd number of particles the normal forms are integrable, which permits us to apply KAM-theory. This leads to the presence of many invariant tori on which the motion is quasi-periodic. Thus we explain the recurrence phenomena and the small size of chaos observed in experiments. Furthermore, we find a certain clustering of modes.

Keywords: Fermi–Pasta–Ulam-chain; Normalisation; KAM-theorem; Recurrence (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:285:y:2000:i:3:p:467-482

DOI: 10.1016/S0378-4371(00)00253-3

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