On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

@article{Morosi1998OnAC,
  title={On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian},
  author={Carlo Morosi and Giorgio Tondo},
  journal={Physics Letters A},
  year={1998},
  volume={247},
  pages={59-64}
}
Abstract It is shown that a class of dynamical systems (encompassing the one recently considered by Calogero [J. Math. Phys. 37 (1996) 1735] is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained through a non-canonical map whose form is directly suggested by the associated Nijenhuis tensor. 
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