Separability theory of Gel'fand-Zakharevich systems on Riemannian manifolds

Abstract:
A complete separability theory of Liouville integrable systems with n quadratic in momenta constants of motion is presented. It is geometric separability theory of Gel'fand-Zakharevich bi-Hamiltonian systems on Riemannian manifolds. We start with the separability of systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then, infinitely many new classes of separable systems are constructed by appropriate deformations of Benenti class systems. All such systems can be lifted to the Gel'fand-Zakharevich bi-Hamiltonian form.