Nekhoroshev theorem for the periodic Toda lattice

Details Nekhoroshev theorem for the periodic Toda lattice Nekhoroshev theorem for the periodic Toda lattice

2008-12-29

arxiv.org/abs/0812.4912v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages

Scientific paper

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 $\R^{N-1}$. 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.

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