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arXiv · hep-th/9407043

Dynamical R-Matrices for Integrable Maps

O. Ragnisco
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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 $r$-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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O. Ragnisco. 1994-07-07. Dynamical R-Matrices for Integrable Maps. https://doi.org/10.1016/0375-9601(95)00056-9

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