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We provide numerical evidence of global diffusion occurring inslightly perturbed integrable Hamiltonian systems and symplectic maps. Weshow that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so-called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems

First numerical evidence of global Arnold diffusion in quasi-integrable systems