Manev problem and its real form dynamics: superintegrability and symmetry algebras. (English) Zbl 1105.37053

Kyuldjiev, Assen; Gerdjikov, Vladimir; Marmo, Giuseppe; Vilasi, Gaetano

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 \(\text{su}(2)\simeq\text{so}(3)\) or \(\text{so}(2,1)\) 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.
For the entire collection see [Zbl 1089.53004].

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

37N05	Dynamical systems in classical and celestial mechanics
70F05	Two-body problems
70G65	Symmetries, Lie group and Lie algebra methods for problems in mechanics
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37J15	Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)

Keywords:

symmetry algebras; superintegrability; Manev model