Bifurcations of plane to 3D periodic orbits in the restricted three-body problem with oblateness

We consider the bifurcation of 3D periodic orbits from the plane of motion of the primaries in the restricted three-body problem with oblateness. The simplest 3D periodic orbits branch-off at the plane periodic orbits of indifferent vertical stability. We describe briefly suitable numerical techniques and apply them to produce the first few such vertical-critical orbits of the basic families of periodic orbits of the problem, for varying mass parameter mu and fixed oblateness coefficent A(1) = 0.005, as well as for varying A(1) and fixed mu = 1/2. The horizontal stability of these orbits is also determined leading to predictions about the stability of the branching 3D orbits.