Proof of Nishida's conjecture on anharmonic lattices
arXiv:nlin/0506024 · doi:10.1007/s00220-005-1451-1
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.
16 pages, 1 figure; accepted for publication in Comm. Math. Phys