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arXiv · 1504.02211

On bi-Hamiltonian formulation of the perturbed Kepler problem

Yu. A. Grigoryev·A. V. Tsiganov
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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.

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Yu. A. Grigoryev, A. V. Tsiganov. 2015-04-09. On bi-Hamiltonian formulation of the perturbed Kepler problem. https://doi.org/10.1088/1751-8113%2F48%2F17%2F175206

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