On the equivalence between Manev and Kepler problems. (English) Zbl 1379.70035

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). Geometry, Integrability and Quantization, 241-251 (2008).
Summary: Here we demonstrate the existence of a local Darboux chart for the Manev model such that its dynamics becomes locally equivalent to the Kepler model. This explains lot of similarities between these two models and especially why they share common symmetry algebras. We also discuss the existence of group actions on the phase space for the algebras inherent in the Manev model.
For the entire collection see [Zbl 1154.17001].


70F05 Two-body problems
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