On a Trivial Family of Noncommutative Integrable Systems

Abstract

Abstract. We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these deformations to construct a new trivial family of noncommutative integrable systems.

On a generalization of systems of Calogero type

“…В случае если u 12 , u 13 , u 12 являются константами, мы получаем известную систему Якоби [4]. Другие частные случаи (2) рассмотрены в работах [2,10]. Уравнения (2) кроме энергии сохраняют полный импульс всей системы…”

Deformations of the Poisson brackets and the Kowalevski top

“…At n = 3 there are enough vector fields and integrals of motion in order to prove integrability of the corresponding dynamical system using the Euler-Jacoby theorem or the Lie integrability theorem [16,33].…”