Bihamiltonian structures and Stäckel separability

@inproceedings{Ibort2000BihamiltonianSA,
  title={Bihamiltonian structures and St{\"a}ckel separability},
  author={Alberto Ibort and Franco Magri and Giuseppe Marmo},
  year={2000}
}
Abstract It is shown that a class of Stackel separable systems is characterized in terms of a Gel’fand–Zakharevich bihamiltonian structure. This structure arises as an extension of a Poisson–Nijenhuis structure on phase space. It is also shown that the Casimir of the Gel’fand–Zakharevich bihamiltonian structure provides the family of commuting Killing tensors found by Benenti and that, because of Eisenhart’s theorem, characterize orthogonal separability. It is also shown that recently found… CONTINUE READING

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