Near-integrability of periodic FPU-chains

The FPU-chain with periodic boundary conditions is studied by Birkhoff-Gust avson normalisation. In the cases of up to 6 particles and for beta-chains with an odd number of particles the normal form are integrable, which permi ts us to apply KAM-theory. This leads to the presence of many invariant tor i on which the motion is quasi-periodic. Thus we explain the recurrence phe nomena and the small size of chaos observed in experiments. Furthermore, we find a certain clustering of modes. (C) 2000 Elsevier Science B.V. All rig hts reserved.