Poincare and the Three-Body Problem

The Three-Body Problem has been a recurrent theme of Poincare's thought. Having understood very early the need for a qualitative study of "non-integrable" differential equations, he developed the necessary fundamental tools: analysis, of course, but also topology, geometry, probability. One century later, mathematicians working on the Three-Body Problem still draw inspiration from his works, in particular in the three volumes of Les methodes nouvelles de la mecanique celeste published respectively in 1892, 1893, 1899.