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Proof of Nishida's Conjecture on Anharmonic Lattices

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Abstract

We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.

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  1. Mathematics Department, Imperial College London, London, SW7 2AZ, UK

    Bob Rink

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  1. Bob Rink
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Correspondence to Bob Rink.

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Communicated by G. Gallavotti

Supported by an EPSRC postdoctoral fellowship.

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Rink, B. Proof of Nishida's Conjecture on Anharmonic Lattices. Commun. Math. Phys. 261, 613–627 (2006). https://doi.org/10.1007/s00220-005-1451-1

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  • DOI: https://doi.org/10.1007/s00220-005-1451-1

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