TITLE: Normal form for a quasi-periodic perturbation of the Sun-Jupiter RTBP. 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 make a local semi-analytical study of a quasi-periodic perturbation of the Sun-Jupiter RTBP Hamiltonian in a neighbourhood of the triangular points. First, we construct a suitable normal form of the Hamiltonian around the invariant torus that replaces $L_5$. Then, we use this (high order) normal form to give a description of the local non-linear dynamics.