@article {2003, title = {Separation of variables for Bi-Hamiltonian systems}, journal = {Math. Phys. Anal. Geom. 6 (2003) 139-179}, number = {SISSA;27/2002/FM}, year = {2003}, publisher = {SISSA Library}, abstract = {We 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.}, doi = {10.1023/A:1024080315471}, url = {http://hdl.handle.net/1963/1598}, author = {Gregorio Falqui and Marco Pedroni} }