Interested in the global dynamical structure of the Jovian irregular satellites and their chaotic evolutions, we have performed numerical integrations of the satellites along with an indicator of chaos (MEGNO), to give a clear representation of the dynamical structure of the regions surrounding the satellites, and the consequences on the individual evolutions of the bodies. In particular, as the long-term integrations give indications about the chaotic diffusion of the satellites in the phase space, dynamical maps show the reasons of the detected chaos and the underlying resonant dynamics acting on the satellite system.