Bogoyavlensky--Volterra and Birkhoff Integrable Systems
Mathematical Physics
2009-11-11 v1 math.MP
Symplectic Geometry
Abstract
In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the cases in the classification of Kozlov and Treshchev of Birkhoff integrable Hamiltonian systems. Using this connection we demonstrate the integrability of the system and define a new Lax pair representation. In addition, we comment on the bi--Hamiltonian structure of the system.
Cite
@article{arxiv.math-ph/0608051,
title = {Bogoyavlensky--Volterra and Birkhoff Integrable Systems},
author = {Pantelis A. Damianou and Stelios P. Kouzaris},
journal= {arXiv preprint arXiv:math-ph/0608051},
year = {2009}
}
Comments
21 pages