Abstract
This paper deals with the planar three-body problem with equal masses and moving under 1/r2 potential. The complete reduction of this problem is done by using its finite group of symmetries and the Jacobi-Maupertuis metric. We show that it is the unfolding of a flow which is topologically conjugate to a geodesic billiard problem with the Jacobi-Maupertuis metric. Finally there is a numerical exploration of the corresponding billiard map.
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