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Zbl 1145.70004
Kyuldjiev, Assen; Gerdjikov, Vladimir; Marmo, Giuseppe; Vilasi, Gaetano
On the symmetries of the Manev problem and its real Hamiltonian form. (English)
[A] Mladenov, Iva\"ilo (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. 221-233 (2007). ISBN 978-954-8495-37-0/pbk

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 ${\germ{so}}(3)$ or ${\germ{so}}(2,1)$ 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.

MSC 2000:: *70F05 Two-body problem
70G65 Symmetries, Lie-group and Lie-algebra methods
70H33 Symmetries

Keywords: Ermanno-Bernoulli invariants; Laplace-Runge-Lenz vector; symmetry algebras

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