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Nonintegrability of the two-body problem in constant curvature spaces

Alexey V. Shchepetilov
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Abstract

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

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Alexey V. Shchepetilov. 2006-10-08. Nonintegrability of the two-body problem in constant curvature spaces. https://doi.org/10.1088/0305-4470/39/20/011

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