Nekhoroshev theorem for the periodic Toda lattice

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

28 pages

References in corpus (3)

• The Fermi-Pasta-Ulam problem: 50 years of progress
• Global Birkhoff coordinates for the periodic Toda lattice
• Global action-angle variables for the periodic Toda lattice

Cited by in corpus (4)

• The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior
• Wave Turbulence and thermalization in one-dimensional chains
• On the role of the Integrable Toda model in one-dimensional molecular dynamics
• On the convexity of the KdV Hamiltonian