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arXiv · 0812.4912

Nekhoroshev theorem for the periodic Toda lattice

Andreas Henrici·Thomas Kappeler
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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 $\R^{N-1}$. 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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Andreas Henrici, Thomas Kappeler. 2008-12-29. Nekhoroshev theorem for the periodic Toda lattice. https://doi.org/10.1063/1.3196783

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