Infinitely Many Eclipses
Richard Montgomery · arXiv (Cornell University) · 2001
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suffer a triple collision. Motivation for the result comes from the dream of building a symbolic dynamics for the three-body problem, one whose symbols 1, 2, 3 representing the three types of eclipses. The proof involves the conformal geometry of the shape sphere.