TY - JOUR

T1 - On bi-Hamiltonian formulation of the perturbed Kepler problem

AU - Grigoryev, Yu A.

AU - Tsiganov, A. V.

PY - 2015

Y1 - 2015

N2 - 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 goes against a necessary condition for the existence of the bi-Hamiltonian structure according to the Fernandes theorem. In fact, the initial and perturbed Kepler systems are both isochronous systems and, therefore, the Fernandes theorem cannot be applied to them.

AB - 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 goes against a necessary condition for the existence of the bi-Hamiltonian structure according to the Fernandes theorem. In fact, the initial and perturbed Kepler systems are both isochronous systems and, therefore, the Fernandes theorem cannot be applied to them.

KW - bi-Hamiltonian geometry

KW - Kepler problem

KW - action-angle variables

U2 - 10.1088/1751-8113/48/17/175206

DO - 10.1088/1751-8113/48/17/175206

M3 - Article

VL - 48

SP - 175206

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

ER -