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

Massimiliano Guzzo (1) , Elena Lega (2) , Claude Froeschle (2)

1 Dipartimento di Matematica Pura e Applicata [Padova]
2 CASSIOPEE - Laboratoire de Cosmologie, Astrophysique Stellaire & Solaire, de Planétologie et de Mécanique des Fluides

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.

Keywords: Arnold diffusion quasi-integrable systems detection of stable/unstable manifolds

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

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⟩