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The increasing number of extra-solar planets opens a new opportunity forstudies of the formation of planetary systems. Resonant systems are ofparticular interest because their dynamical configuration provides constraintson the unobservable formation and migration phase. In this thesis, formationscenarios for the planetary systems HD128311 and HD45364 are presented. N-bodysimulations of two planets and two dimensional hydrodynamical simulations ofproto-planetary discs are used to model the migration phase and the captureinto resonance. The results indicate that the proto-planetary disc has a largersurface density than previously thought. Proto-planets are exposed tostochastic forces, generated by density fluctuations in the disc. A genericmodel of both a single planet, and two planets in resonance, beingstochastically forced is presented. The system GJ876, for example, is stablefor reasonable strengths of the stochastic forces, but systems with lighterplanets can get disrupted. Even if they are not disrupted completely,stochastic forces create characteristic, observable libration patterns.Turbulence plays also an important role during the early phases of the planetformation process. Due to the large separation of scales, the gravitationalcollapse in the core accretion model is very hard to model numerically. Ascaled method is presented, that allows for the correct treatment ofself-gravity in a marginally collisional system by taking into account therelevant small scale processes. Interestingly, this system is dynamically verysimilar to Saturn's rings. The stochastic migration of small bodies in Saturn'srings is also studied. Analytic predictions of the interactions of amoonlet/propeller with ring particles are compared to collisional N-bodysimulations with up to a million particles. The random walk is fast enough tobe directly observable by the Cassini spacecraft.

The effects of stochastic forces on the evolution of planetary systems and Saturn's rings