A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems.
Abstract
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.
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