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.

中文翻译：

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三体问题作为具有奇点的测地台球图

本文研究等质量且在1 / r ²势下运动的平面三体问题。通过使用对称的有限组和Jacobi-Maupertuis度量，可以完全解决此问题。我们表明，与Jacobi-Maupertuis测度的测地台球问题在拓扑上共轭的是流动的展开。最后，对相应的台球图进行了数值探索。