Continuation of periodic orbits: Three-dimensional circular restricted to the general three-body problem

It is proved that a periodic orbit of the three-dimensional circular restricted three-body problem can be continued analytically, when the mass of the third body is sufficiently small, to a periodic orbit of the three dimensional general three-body problem in a rotating frame. The above method is not applicable when the period of the periodic orbit of the restricted problem is equal to 2k (k any integer), in the usual normalized units. Several numerical examples are given.