Yury Grigoryev

On bi-Hamiltonian formulation of the perturbed Kepler problem

The perturbed Kepler problem is shown to be a bi-Hamiltonian system in the domain of definition of the action-angle variables. The graph of the corresponding Hamilton function is not a hypersurface of translation and, therefore, it constitutes a counterexample to the original Fernandes theorem about the necessary and sufficient conditions for the existance of bi-Hamiltonian structures around a Liouville torus.