A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems. - INSU - Institut national des sciences de l'Univers Access content directly
Preprints, Working Papers, ... Year : 2009

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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Dates and versions

insu-00186175 , version 1 (12-11-2007)
insu-00186175 , version 2 (27-01-2009)

Identifiers

  • HAL Id : insu-00186175 , version 2

Cite

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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