Dynamics in the exterior 2 : 3 resonance with Neptune

We study the dynamical behaviour of the exterior 2 : 3 resonance with Neptune, by means of semi-analytical and numerical tools. The libration laws for the planar case are obtained including the long-term effects of the other perturbing planets. They give the basic properties of the small amplitude librations. We are concerned not only with librations around σ = 180°, but also with the librations around σ = 0°. In the frame of the elliptic planar restricted three-body problem we construct surfaces of sections and we discuss the effect of including other perturbers. Finally, a numerical integration of several particles in the three-dimensional outer Solar System is performed, aiming at an empirical analysis of the resonance characteristics. We define the region of the phase space of initial conditions that generates stable librations. Secular resonances are also analyzed, as well as the mechanisms that render the resonant motion unstable.