Quasi-periodic Solutions for the three-body problem

A rigorous proof of the existence of a class of quasi-periodic solutions of the three-body problem is given. Each of the bodies moves in a nearly circular inclined orbit around the center of mass. The solutions ob- tained possess, in addition to the nodal frequency, two or three rationally independent frequencies, that is, the number of frequencies is less than the number of degrees of freedom. Two main cases are discussed, the planetary, where one mass dominates the system, and the lunar, where the ratio of the semimajor axes is very small. Certain limiting cases, such as the restricted problem, are also discussed.