Separation of Variables for Bi-Hamiltonian Systems

@article{Falqui2002SeparationOV,
  title={Separation of Variables for Bi-Hamiltonian Systems},
  author={Gregorio Falqui and Marco Pedroni},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2002},
  volume={6},
  pages={139-179}
}
  • G. Falqui, M. Pedroni
  • Published 2002
  • Mathematics, Physics
  • Mathematical Physics, Analysis and Geometry
We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called ωN manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the ωN manifold itself. We apply these results to bi-Hamiltonian systems of the Gel… Expand
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TLDR
It is shown that linear separation relations are fundamental objects for integration by quadratures of Stâckel-separable Liouville-integrable systems (the so-called Stäckel systems) and implies that the existence of bi-Hamiltonian representation of LiouVILLE-integRable systems is a necessary condition for StäCkel separability. Expand
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