Three dimensional periodic orbits in exterior mean motion resonances with Neptune

In the framework of the three dimensional restricted three-body problem we study the dynamics of the exterior mean motion resonances with Neptune. The basis of our study is the computation of periodic orbits and their linear stability. The position and stability of periodic orbits critically determine the phase space topology. Stable periodic orbits are centers of regular librations where resonant trapping of minor bodies can take place. The periodic orbits are continued analytically from the planar model to the three-dimensional one forming families, which, in most cases, extend up to high inclination values and pass to the regime of retrograde motion. A classification of the families, according to their continuation and termination, is given. The computations show that resonant librating motion is present up to high inclination values and for particular eccentricity domains. When the ellipticity of the Neptune's orbit is taken into account, periodic orbits are found only for very high inclination values and all of them are unstable.