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Manev problem and its real form dynamics: superintegrability and symmetry algebras. (English) Zbl 1105.37053
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 203-217 (2006).
The authors show that the Manev model possesses Ermano-Bernoulli-type invariants and symmetry algebras $\text{su}\left(2\right)\simeq \text{so}\left(3\right)$ or $\text{so}\left(2,1\right)$ in addition to the angular momentum algebra. These two facts indicate that the Manev model provides better description of the real motion of the heavenly bodies than the Kepler model and in the same times, it shares its most celebrated mathematical features: its superintegrability and large symmetry algebras.
##### MSC:
 37N05 Dynamical systems in classical and celestial mechanics 70F05 Two-body problems 70G65 Symmetries, Lie-group and Lie-algebra methods for dynamical systems 37J35 Completely integrable systems, topological structure of phase space, integration methods 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
##### Keywords:
symmetry algebras; superintegrability; Manev model