Classification of periodic orbits in the four- and five-body problems.

The research described in this paper was motivated by the new types of periodic solutions that were recently discovered by Moore, Chenciner, Montgomery, and Simo in the three-body and the N-body problem (with large N). We attempt to classify the various types of periodic orbits, in the inertial frame, on the basis of an extensive numerical exploration. We have started an exploration of the four-body problem, where the classification of types of periodic orbits is more involved.