國立清華大學 數學系

Abstract: In an unpublished paper by Richard Montgomery, the author claimed to prove the existence of Figure 8 solutions of the Newtonian three body problem with two equal masses ( The solutions look like a figure 8 in the shape space. It is different from the famous figure 8 solution proved by Chenciner and Montgomery where all the three masses are equal). However there is an error in the proof and the problem is still open. In this talk we show that if the gravity is a weak force stronger than the Newtonian, then the approach laid out by Montgomery can be carried out and such Figure 8 solutions do exist.