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arXiv · 0904.2070

Bi-Hamiltonian representation of Stäckel systems

Maciej Blaszak
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Abstract

It is shown that a 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 {\em 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.

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Maciej Blaszak. 2009-04-14. Bi-Hamiltonian representation of Stäckel systems. https://doi.org/10.1103/physreve.79.056607

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