The Toda lattice is super-integrable

TL;DR

This paper proves that the classical, non-periodic Toda lattice is super-integrable by demonstrating it has 2N-1 independent constants of motion using special action-angle coordinates.

Contribution

It establishes the super-integrability of the Toda lattice, providing a rigorous proof and utilizing Moser's action-angle coordinates.

Findings

The Toda lattice has 2N-1 independent constants of motion.

The proof employs special action-angle coordinates introduced by Moser.

The result confirms the super-integrability of the classical Toda lattice.

Abstract

We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action--angle coordinates introduced by Moser to solve the equations of motion.