Resonances in the asteroid and trans-Neptunian belts: A brief review

Mean motion resonances play a fundamental role in the dynamics of the small bodies of the Solar System. The last decades of the 20th century gave us a detailed description of the dynamics as well as the process of capture of small bodies in coplanar or small inclination resonant orbits. More recently, semianalytical or numerical methods allowed us to explore the behavior of resonant motions for arbitrary inclination orbits. The emerging dynamics is very rich, including large orbital changes due to secular effects inside mean motion resonances. The process of capture in highly inclined or retrograde resonant orbits was addressed showing that the capture in retrograde resonances is more efficient than in direct ones. A new terminology appeared in order to characterize the properties of the resonances. Numerical explorations in the transneptunian region showed the relevance and the particular dynamics of the exterior resonances with Neptune which can account for some of the known high perihelion orbits in the scattered disk. Moreover, several asteroids evolving in resonance with planets other than Jupiter or Neptune were found and a large number of asteroids in three-body resonances were identified.