Open Access
VOL. 6 | 2005 On Superintegrability of the Manev Problem and its Real Hamiltonian Form
Assen Kyuldjiev, Vladimir Gerdjikov, Giuseppe Marmo, Gaetano Vilasi

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2005: 262-275 (2005) DOI: 10.7546/giq-6-2005-262-275


We construct Ermanno–Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of the Laplace–Runge–Lenz vector in the Kepler model. If the orbits are bounded these invariants exist only when a certain rationality condition is met and thus we have superintegrability only on a subset of initial values. Manev model’s dynamics is demonstrated to be bi-Hamiltonian and a recursion operator is constructed. We analyze real form dynamics of the Manev model and derive that it is always superintegrable. We also discuss the symmetry algebras of the Manev model and its real Hamiltonian form.


Published: 1 January 2005
First available in Project Euclid: 12 June 2015

zbMATH: 1136.70318
MathSciNet: MR2161773

Digital Object Identifier: 10.7546/giq-6-2005-262-275

Rights: Copyright © 2005 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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