2-Dimensional invariant tori for the spatial isosceles 3-body problem

Abstract

We consider the circular Sitnikov problem as a special case of the restricted spatial isosceles 3-body problem. In appropriate coordinates we show the existence of 2-dimensional invariant tori that are formed by union of either periodic or quasiperiodic orbits of the circular Sitnikov problem, these tori are not KAM torio We prove that such invariant tori persist when we consider the spatial isosceles 3-body problem for sufficiently small values of one of the masses. The main tool for proving these results is the analytic continuation method of periodic orbits.