TITLE: Restricted four and five-body problems in the Solar system AUTHORS: Frederic Gabern and Angel Jorba Departament de Matematica Aplicada i Analisi Universitat de Barcelona Gran Via 585 08007 Barcelona, Spain E-mails: gabern@mat.ub.es, angel@maia.ub.es ABSTRACT: We focus on the dynamics of a small particle near the Lagrangian points of the Sun-Jupiter system. To try to account for the effect of other planets, such as Saturn or Uranus, we develop specific models based on the numerical computation of periodic and quasi-periodic (with two frequencies) solutions of the N-body problem and write them as perturbations of the Sun-Jupiter restricted Three Body Problem.