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

Abstract

We consider the reduced two-body problem with a central potential on the sphere ${\mathbf{S}}^2$ and the hyperbolic plane ${\mathbf{H}}^2$. 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.

10 pages