Resonances and stability of extra-solar planetary systems

This paper reviews recent results on the dynamics of multiple-planet extra-solar systems, including main sequence stars and the pulsar PSR B1257+12 and, comparatively, our own Solar System. Taking into account the degree of gravitational interaction of the planets, the known planetary systems may be separated into four main groups: (Ia) Planets in Mean-motion resonance (Ib) Low-eccentricity near-resonant pairs; (II) Non-resonant planets with a significant secular dynamics; and (III) Weakly interacting planet pairs. Different analytical and numerical tools can help to understand the structure of the phase space, to identify stability mechanisms and to categorize different types of motions in the cases of more significant dynamical interaction. The origin of resonant configurations is discussed in the light of the hypothesis of planetary migration.