%0 Unpublished work %T A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems. %+ Dipartimento di Matematica Pura e Applicata [Padova] %+ Laboratoire de Cosmologie, Astrophysique Stellaire & Solaire, de Planétologie et de Mécanique des Fluides (CASSIOPEE) %A Guzzo, Massimiliano %A Lega, Elena %A Froeschle, Claude %8 2009-01-20 %D 2009 %K Arnold diffusion quasi-integrable systems detection of stable/unstable manifolds %Z Physics [physics]/Mathematical Physics [math-ph] %Z Mathematics [math]/Mathematical Physics [math-ph]Preprints, Working Papers, ... %X We investigate numerically the stable and unstable manifolds of the hyperbolic manifolds of the phase space related to the resonances of quasi-integrable systems in the regime of validity of the Nekhoroshev and KAM theorems. Using a model of weakly interacting resonances we explain the qualitative features of these manifolds characterized by peculiar 'flower--like' structures. We detect different transitions in the topology of these manifolds related to the local rational approximations of the frequencies. We find numerically a correlation among these transitions and the speed of Arnold diffusion. %G English %2 https://insu.hal.science/insu-00186175v2/document %2 https://insu.hal.science/insu-00186175v2/file/fiorimod2.pdf %L insu-00186175 %U https://insu.hal.science/insu-00186175 %~ INSU %~ UNICE %~ CNRS %~ INSMI %~ OCA %~ CASSIOPEE %~ TDS-MACS %~ UNIV-COTEDAZUR