Nonintegrability of the two-body problem in constant curvature spaces

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

2006-01-16

arxiv.org/abs/math/0601382v3

J. Phys. A: Math. Gen. V. 39 (2006), pp. 5787-5806

Mathematics

Dynamical Systems

20 pages, typos corrected

Scientific paper

10.1088/0305-4470/39/20/011

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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