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We investigate the dynamics of small trojan exoplanets in domains ofsecondary resonances within the tadpole domain of motion. We consider the limitof a massless trojan companion of a giant planet. Without other planets, thisis a case of the elliptic restricted three body problem (ERTBP). The presenceof more planets (the restricted multi-planet problem, RMPP) induces new directand indirect secular effects on the trojan's dynamics. In the theoretical partof this paper, we develop a Hamiltonian formalism in action-angle variables,which allows to treat in a unified way resonant dynamics and secular effects onthe trojan body in both the ERTBP or the RMPP. Our formalism leads to adecomposition of the Hamiltonian in two parts, $H=H_b+H_{sec}$. $H_b$, calledthe basic model, describes resonant dynamics in the short-period (epicyclic)and synodic (libration) degrees of freedom. $H_{sec}$ contains only termsdepending on slow (secular) angles. $H_b$ is formally identical in the ERTBPand the RMPP, apart from a re-definition of angular variables. An importantphysical consequence is that the slow chaotic diffusion proceeds in both theERTBP and the RMPP by a qualitatively similar dynamical mechanism betterapproximated by the paradigm of `modulational diffusion'. In the numericalpart, we focus on the ERTBP for making a numerical demonstration of the chaoticdiffusion process along resonances. Using color stability maps, we provide asurvey of the resonant web for characteristic mass parameters of the primary,in which the secondary resonances from 1:5 to 1:12 (ratio of the short over thesynodic period) and their resonant multiplets appear. We give numericalexamples of diffusion of weakly chaotic orbits in the resonant web. We make astatistics of the escaping times in the resonant domain, and find power-lawtails of the distribution of escaping times for slowly diffusing chaoticorbits.

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems