Backlund transformations for many-body systems related to KdV

We present Backlund transformations (BTs) With parameter for certain classi cal integrable n-body systems, namely the many-body generalized Henon-Heile s, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considere d as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact tim e-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality prope rty with respect to the Backlund parameter.