The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

TL;DR

This paper proves the integrability of the final unresolved case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems using a modified Lax pair approach.

Contribution

It introduces a novel modification of the quadratic Lax pair method to establish integrability for the last open case in the classification.

Findings

Confirmed integrability of the last Kozlov-Treshchev case

Extended Lax pair techniques to new Hamiltonian systems

Demonstrated the applicability of Ranada's method in this context

Abstract

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.