Stabilit\'e orbitale pour le syst\`eme de Vlasov-Poisson gravitationnel

This paper reviews the recent mathematical progresses made on the study of the orbital stability properties for the gravitational Vlasov-Poisson system. We present in details the paper of Lemou, M'ehats and Rapha"el (Inventiones 2011) and we review also the previous works by Dolbeault, Guo, Hadzic, Lin, Rein, S'anchez, Soler, Wan, Wolansky. We also include a discussion of the history of this topic and the pioneering works by physicists like Antonov, Lynden-Bell and Aly. This is the text of a Bourbaki seminar given in november 2011