This work is based on Papaloizou's review paper (2003) published in Celestial Mechanics and Dynamical Astronomy (vol 87), which models a planetary system composed of a star and a disk of dust, in which two planets are blocked in a 2:1 resonance.
The motivation for the construction of such models derives from the recent detection of a hundred of exoplanets, moving around faraway stars, and very often blocked two by two in situation of orbital resonance. The presence of disks of dust around the star can explain, in some cases, the capture of those huge planets (larger than Jupiter) on orbits highly close to the star.
The master thesis consists in rebuilding the equations of the resonant dynamics, in analyzing its equilibria and in comparing them with a series of numerical simulations published by the same author. The theoretical framework is the three body problem, planar and averaged on the non-resonant short periods; a dissipation due to the disk is introduced on the motion of the outer planet, connected with typical circularization and migration times. The agreement between analytical results (obtained with the simplified model) and the numerical simulations (based on the equations of the mechanics of fluids) is not perfect and has led to a critical study.