In this paper we discuss the relevance of diffusive processes in multidimensional Hamiltonian systems. By means of a rather simple model, we present evidence that for moderate-to-strong chaotic systems the stochastic motion remains confined to disjoint domains on the energy surface, at least for mild motion times. We show that only for extremely large timescales and for rather large perturbations, does the chaotic component appear almost fully connected through the relics of the resonance structure. The discussion whether diffusion over the energy surface could actually occur in asteroidal or galaxy dynamics is also included.Facultad de Ciencias Astronómicas y Geofísica
