Nonintegrability of the two-body problem in constant curvature spaces

Abstract

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

20 pages, typos corrected

References in corpus (1)

• Two body problem on two point homogeneous spaces, invariant differential operators and the mass center concept

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