标题： 可积映射的动力学R-矩阵 显示英文标题

标题： Dynamical R-Matrices for Integrable Maps

摘要： 基于 Lax 表示，利用$r$-矩阵方法建立了两个辛映射的可积性，这两个辛映射可以看作是 Garnier 和 Neumann 系统的离散时间类比。与连续情形不同，这类离散系统的$r$-矩阵被证明是动力学类型的；值得注意的是，诱导出的泊松结构表现为一些相容的“更基本”泊松结构的线性组合。还表明，Lax 矩阵自然地引出了分离变量，并研究了这些变量的离散和连续动力学。 显示英文摘要

摘要： 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.