A TIME-DISCRETIZED VERSION OF THE CALOGERO-MOSER MODEL

We introduce an integrable time-discretized version of the classical C alogero-Moser model, which goes to model in a continuum limit. This di screte model is obtained from pole solutions of a discretized version of the Kadomtsev-Petviashvili equation, leading to a finite-dimensiona l symplectic mapping. Lax pair, symplectic structure and sufficient se t of invariants of the discrete Calogero-Moser model are constructed. The classical r-matrix is the same as for the continuum model. An exac t solution of the initial value problem is given.