On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top
Mathematical Physics
2007-07-31 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
This paper deals with a remarkable integrable discretization of the so(3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streamlined presentation of their results, we provide a bi-Hamiltonian structure for this discretization, thus proving its integrability in the standard Liouville-Arnold sense.
Keywords
Cite
@article{arxiv.0707.4382,
title = {On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top},
author = {Matteo Petrera and Yuri B. Suris},
journal= {arXiv preprint arXiv:0707.4382},
year = {2007}
}
Comments
11 pages