Dynamical R-Matrices for Integrable Maps
High Energy Physics - Theory
2009-10-28 v1 Exactly Solvable and Integrable Systems
solv-int
Abstract
The integrability of two symplectic maps, that can be considered as discrete-time analogs of the Garnier and Neumann systems is established in the framework of the -matrix approach, starting from their Lax representation. In contrast with the continuous case, the -matrix for such discrete systems turns out to be of dynamical type; remarkably, the induced Poisson structure appears as a linear combination of compatible ``more elementary" Poisson structures. It is also shown that the Lax matrix naturally leads to define separation variables, whose discrete and continuous dynamics is investigated.
Cite
@article{arxiv.hep-th/9407043,
title = {Dynamical R-Matrices for Integrable Maps},
author = {O. Ragnisco},
journal= {arXiv preprint arXiv:hep-th/9407043},
year = {2009}
}
Comments
16 plain tex pages