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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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https://hal-insu.archives-ouvertes.fr/insu-00186175
Contributor : Elena Lega <>
Submitted on : Tuesday, January 27, 2009 - 10:07:56 AM
Last modification on : Monday, October 12, 2020 - 11:10:15 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 11:46:12 AM

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  • HAL Id : insu-00186175, version 2

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Massimiliano Guzzo, Elena Lega, Claude Froeschle. A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems.. 2009. ⟨insu-00186175v2⟩

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