Dynamical R-Matrices for Integrable Maps

Details Dynamical R-Matrices for Integrable Maps Dynamical R-Matrices for Integrable Maps

1994-07-07

arxiv.org/abs/hep-th/9407043v1

Physics

High Energy Physics

High Energy Physics - Theory

16 plain tex pages

Scientific paper

10.1016/0375-9601(95)00056-9

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 $r$-matrix approach, starting from their Lax representation. In contrast with the continuous case, the $r$-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.

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