On bi-Hamiltonian formulation of the perturbed Kepler problem

Abstract

The perturbed Kepler problem is shown to be a bi-Hamiltonian system in spite of the fact that the graph of the Hamilton function is not a hypersurface of translation, which is against a necessary condition for the existence of the bi-Hamiltonian structure according to the Fernandes theorem. In fact, both the initial and perturbed Kepler systems are isochronous systems and, therefore, the Fernandes theorem cannot be applied to them.

7 pages, LaTeX with AMS fonts

References in corpus (1)

• A simple way of making a Hamiltonian system into a bi-Hamiltonian one