Dynamical study of the exoplanets and debris disks revealed by SPHERE

Several decades after the discovery of the first debris disks and exoplanets, lots of questions remain regarding the mechanisms of formation and evolution of planetary systems. The recent progress of high-resolution high-contrast direct imaging, illustrated by the instruments VLT/SPHERE and Gemini/GPI, enables to unveil the outer architecture (> 5 au) of young (< 200 Myr) extrasolar systems when the dynamical interactions are frequent. This work sheds light on the origin and dynamical evolution mechanisms of planetary systems through the detailed study of key systems resolved with SPHERE and through the developing of dedicated tools.The first part of this manuscript tackles the subject of N-body simulations. Numerous algorithms have been proposed and implemented, with different compromises on their speed, accuracy, and versatility. Among these algorithms, SWIFT HJS allows us to model for secular times architectures that are very different from our Solar System. It is thus an essential tool to the study of planetary to stellar companions with non-negligible mass ratio, which are often encountered with direct imaging. Within my Ph.D., the functionalities of the algorithm were extended to handle hierarchy changes and close encounters, which can play an important part in the dynamical history of planetary systems. The code was used to study in detail the mysterious system HD 106906, in particular, the interactions between its main components (binary star, planet, debris disk).In the second part of the manuscript, I introduce the subject of orbital fitting. The observation of a system at different epochs allows theoretically to retrieve the characteristics of the orbits. However, the problem is often complex and degenerate, in particular when the observations span a small fraction of the orbital period. The widely used MCMC statistical approach enables to get robust estimates in most of the cases. These estimates are then used to study the history and stability of the system, and the interactions between the orbits and their environment, notably the disks. This role of orbital fitting is here illustrated by the study of several benchmark systems imaged with SPHERE.