Abstract
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N−1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of RN−1. We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev’s theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).
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