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

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16 plain tex pages