First numerical evidence of global Arnold diffusion in quasi-integrable systems

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August 2005, 5(3): 687-698. doi: 10.3934/dcdsb.2005.5.687

First numerical evidence of global Arnold diffusion in quasi-integrable systems

Claude Froeschlé ^1, , Massimiliano Guzzo ^2, and Elena Lega ^1,

1.	Observatoire de la Côte d'Azur, Bv. de l'Observatoire, B.P. 4229, 06304 Nice cedex 4, France, France
2.	Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Belzoni 7, 35131 Padova, Italy

Received July 2004 Revised December 2004 Published May 2005

Abstract
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We provide numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We show that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so-called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems.

Keywords: Quasi-integrable systems, Arnold diffusion..

Mathematics Subject Classification: Primary: 37J40, 70K4.

Citation: Claude Froeschlé, Massimiliano Guzzo, Elena Lega. First numerical evidence of global Arnold diffusion in quasi-integrable systems. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 687-698. doi: 10.3934/dcdsb.2005.5.687

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