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Loose ends in a strong force 3-body problem. (English) Zbl 1434.70033

Summary: Up to symmetries, the orbits of three equal masses under an inverse cube force with zero angular momentum and constant moment of inertia can be reparametrized as the geodesics of a complete, negatively curved metric on a pair of pants. The ends of the pants represent binary collisions. Here we will examine the visibility properties of such negatively curved surfaces, allowing a description of orbits beginning or ending in binary collisions of this 3-body problem.

MSC:

70F07 Three-body problems
37N05 Dynamical systems in classical and celestial mechanics
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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References:

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