Integrable discretizations of the spin Ruijsenaars-Schneider models
  Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time counterparts. Explicit solutions are obtained for arbitrary flows of the hierarchies, including the discrete time ones. 
O.Ragnisco (Rome), Yu.B.Suris (Bremen)