LAX REPRESENTATION FOR RESTRICTED FLOWS OF THE KDV HIERARCHY AND FOR THE KEPLER-PROBLEM

We derive a spectral parameter dependent 2 x 2 matrix Lax pair for restricted flows of the KdV hierarchy. Explicit formulas are given for the Neumann, Gamier and the KdV (m = 2) restricted system. A simple generalization provides Lax pairs for the Jacobi and Neumann families of integrable potentials and for all spherically symmetric potentials. In particular the Lax representation for the Kepler problem is found