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.

arXiv comment7 pages, LaTeX with AMS fonts

References in corpus (1)

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

Cited by in corpus (1)

• The Kepler problem: polynomial algebra of non-polynomial first integrals