TITLE: The resonant structure of Jupiter's Trojan asteroids I: Long term stability and diffusion AUTHORS: P. Robutel^(1) and F. Gabern^(2) (1) Astronomie et Systemes Dynamiques IMCCE-Observatoire de Paris 77 Av. Denfert-Rochereau 75014 Paris, France (2) Departament de Matematica Aplicada I Universitat Politecnica de Catalunya Diagonal 647 08028 Barcelona, Spain E-mails: robutel@imcce.fr, frederic.gabern@upc.edu ABSTRACT: We study the global dynamics of the jovian Trojan asteroids by means of the Frequency Map Analysis. We find and classify the main resonant structures that serve as skeleton of the phase space near the Lagrangian points. These resonances organize and control the long-term dynamics of the Trojans. Besides the secondary and secular resonances, that have already been found in other asteroid sets in mean motion resonance (e.g. Main belt, Kuiper belt), we identify a new type of resonance that involves secular frequencies and the frequency of the Great Inequality, but not the libration frequency. Moreover, this new family of resonances plays an important role in the slow transport mechanism that drives Trojans from the inner stable region to eventual ejections. Finally, we relate this global view of the dynamics with the observed Trojans, identify the asteroids that are close to these resonances and study their long-term behaviour.