Separable bi-Hamiltonian systems with quadratic in momenta first integrals

Details Separable bi-Hamiltonian systems with quadratic in momenta first integrals Separable bi-Hamiltonian systems with quadratic in momenta first integrals

2003-12-11

arxiv.org/abs/nlin/0312025v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

53 pages

Scientific paper

Geometric separability theory of Gel'fand-Zakharevich bi-Hamiltonian systems on Riemannian manifolds is reviewed and developed. Particular attention is paid to the separability of systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then, infinitely many new classes of separable systems are constructed by appropriate deformations of Benenti class systems. All such systems can be lifted to the Gel'fand-Zakharevich bi-Hamiltonian form.

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