Secular theories and orbital dynamics beyond Neptune

The dynamical structure of the trans-Neptunian region is still far from being fully understood, especially concerning high-perihelion objects. The major part of this work is focussed on the development of secular models, used to describe the orbital dynamics of trans-Neptunian objects both in the non-resonant and resonant cases. One-degree-of-freedom systems can be obtained, which allows to represent any trajectory by a level curve of the Hamiltonian. Such a formalism is very efficient to explore the parameter space. It reveals pathways to high perihelion distances, as well as “trapping mechanisms”, able to maintain the objects on very distant orbits for billions of years. The application of the resonant secular model to the known objects is also very informative, since it shows graphically which observed orbits require a complex scenario (as the planetary migration or an external perturber), and which ones can be explained by the influence of the known planets. The last part of this work is devoted to the extension of the non-resonant secular model to the case of an external massive perturber. If it has a substantial eccentricity and/or inclination, it introduces one or two more degrees of freedom in the system, so the secular dynamics is non integrable in general. In that case, the analysis can be realised by Poincaré sections, which allows to distinguish the chaotic regions of the phase space from the regular ones.