Separable bi-Hamiltonian systems with quadratic in momenta first integrals

Abstract

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.

53 pages

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Cited by in corpus (4)

• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
• A class of Poisson-Nijenhuis structures on a tangent bundle
• Systematic construction of separable systems with quadratic in momenta first integrals