00998nas a2200121   4500008004100000245005500041210005400096260001800150520063200168100002100800700001900821856003600840       2003                        en  d00aSeparation of variables for Bi-Hamiltonian systems0 aSeparation of variables for BiHamiltonian systems  bSISSA Library3 aWe address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.1 aFalqui, Gregorio1 aPedroni, Marco  uhttp://hdl.handle.net/1963/1598