I will show how boundary value continuation software can be used to compute families of periodic solutions of conservative systems. A very simple example will be used to illustrate the main idea. I will also show how the computational approach can be generalized to follow the recently discovered figure-8 orbit of Montgomery, Chenciner, and Simo, as the mass of one of the bodies is varied. The numerical results show, among other things, that there exist continuous paths from the figure-8 orbit to periodic solutions of the restricted three-body problem.

This is joint work with Randy Paffenroth and Herb Keller at Caltech, Andre Vanderbauwhede in Gent, and Jorge Galan in Sevilla.