SEPARATION OF VARIABLES FOR THE RUIJSENAARS SYSTEM

We construct a separation of variables for the classical n-particle Ru ijsenaars system (the relativistic analog of the elliptic Calogero-Mos er system). The separated coordinates appear as the poles of the prope rly normalised eigenvector (Baker-Akhiezer function) of the correspond ing Lax matrix. Two different normalisations of the BA functions are a nalysed. The canonicity of the separated variables is verified with th e use of the r-matrix technique. The explicit expressions for the gene rating function of the separating canonical transform are given in the simplest cases n = 2 and n = 3. Taking the nonrelativistic limit we a lso construct a separation of variables for the elliptic Calogero-Mose r system.