A class of Liouville-integrable Hamiltonian systems with two degrees of freedom

A class of two-dimensional Liouville-integrable Hamiltonian systems is stud ied. Separability of the corresponding Hamilton-Jacobi equation for these s ystems is shown to be equivalent to other fundamental properties of Hamilto nian systems, such as the existence of the Lax and bi-Hamiltonian represent ations of certain fixed types. Applications to physical models, including t he Calogero-Moser model, an integrable case of the Henon-Heiles potential a nd the nonperiodic Toda lattice are presented. (C) 2000 American Institute of Physics. [S0022-2488(00)01110-5].