## On the symmetries of the Manev problem and its real Hamiltonian form.(English)Zbl 1145.70004

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 221-233 (2007).
Summary: The Manev model and its real form dynamics are known to possess Ermanno-Bernoulli type invariants similar to Laplace-Runge-Lenz vector of Kepler model. Using these additional invariants, we demonstrate here that both Manev model and its real Hamiltonian form possess the same $${\mathfrak{so}}(3)$$ or $${\mathfrak{so}}(2,1)$$ symmetry algebras (in addition to the angular momentum algebra) on angular momentum level sets. Thus Kepler and Manev models are shown to have identical symmetry algebras and hence sharing more features than previously expected.
For the entire collection see [Zbl 1108.53003].

### MSC:

 70F05 Two-body problems 70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics