title: Bi-Hamiltonian representation of Stäckel systems.
abstract: It is shown that linear separation relations are fundamental objects for integration by quadratures of Stäckel-separable Liouville-integrable systems (the so-called Stäckel systems). These relations are further employed for the classification of Stäckel systems. Moreover, we prove that any Stäckel-separable Liouville-integrable system can be lifted to a bi-Hamiltonian system of Gel'fand-Zakharevich type. In conjunction with other known result this implies that the existence of bi-Hamiltonian representation of Liouville-integrable systems is a necessary condition for Stäckel separability.
authors.affiliation: Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland.
authors.forename: Maciej
authors.initials: M
authors.lastname: Błaszak