Poincaré's discovery of homoclinic points.

Nowadays, homoclinic points figure prominently in the study of "chaotic" motions of dynamical systems. Henri Poincaré first encountered homoclinic points in 1889 in connection with his work on the three-body problem of celestial mechanics. The discovery was made under rather dramatic circumstances just as the printing was completed of the famous memoir for which he had been awarded a prize by the Swedish king Oscar II. At the Mittag-Leffler Institute outside Stockholm are kept documents from which one can obtain a clear picture of what actually happened. The purpose of this article is to give publicity to these documents and thereby throw some light on this episode. In particular, it will become clear what Poincaré originally was aiming at in his attack on the three-body problem.