Phys. Rev. E 79, 056607 (2009) [9 pages]Bi-Hamiltonian representation of Stäckel systemsReceived 5 February 2009; published 18 May 2009 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. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.79.056607
DOI:
10.1103/PhysRevE.79.056607
PACS:
45.20.Jj, 02.30.Ik, 45.10.Na
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