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Pré-Publication, Document De Travail Année : 2007

A numerical study of the topology of hyperbolic manifolds supporting diffusion in a priori unstable systems.

Résumé

Using new numerical methods we detect the topology of hyperbolic manifolds supporting diffusion in the a priori unstable dynamical systems and compare them with the diffusion properties. We measure a spread of the asymptotic manifolds which is significant to explain diffusion. We show that the stable and unstable manifolds have a topological transition when the Melnikov approximation looses its accuracy. This transition is correlated to a change of the law of dependence of the diffusion coefficient on the perturbing parameter. This suggests that the Melnikov approximation is not only a technical tool which allows one to compute accurate approximations of the manifolds at small values of the perturbing parameters, but is related to a dynamical regime.
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Dates et versions

insu-00186172 , version 1 (12-11-2007)
insu-00186172 , version 2 (12-01-2009)

Identifiants

  • HAL Id : insu-00186172 , version 1

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Elena Lega, Massimiliano Guzzo, Claude Froeschle. A numerical study of the topology of hyperbolic manifolds supporting diffusion in a priori unstable systems.. 2007. ⟨insu-00186172v1⟩
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