Non-Hamiltonian systems separable by Hamilton-Jacobi method

Details Non-Hamiltonian systems separable by Hamilton-Jacobi method Non-Hamiltonian systems separable by Hamilton-Jacobi method

2007-07-07

arxiv.org/abs/0707.1113v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, LaTeX, no figures

Scientific paper

10.1016/j.geomphys.2007.12.008

We show that with every separable calssical Stackel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These system are known as bi-cofactor systems and are integrable in quadratures as the seed Hamiltonian system is. We show that with each class of bi-cofactor systems a pair of separation curves can be related. We also investigate conditions under which a given flat bi-cofactor system can be deformed to a family of geodesically equivalent flat bi-cofactor systems.

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