  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.

High Energy Physics - Theory;Exactly Solvable and Integrable Systems;Exactly Solvable and Integrable Systems