Nonintegrability of the two-body problem in constant curvature spaces II

Details Nonintegrability of the two-body problem in constant curvature spaces II Nonintegrability of the two-body problem in constant curvature spaces II

2006-11-13

arxiv.org/abs/math/0611373v1

Proceedings of the 5th International Conference Bolyai-Gauss-Lobachevsky (Minsk, October 10-13, 2006) Editors: Yu. Kurochkin,

Mathematics

Dynamical Systems

10 pages

Scientific paper

We consider the reduced two-body problem with a central potential on the
sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For two potentials
different from the Newton and the oscillator ones we prove the nonexistence of
an additional meromorphic integral for the complexified dynamic systems.

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