First numerical evidence of global Arnold diffusion inquasi-integrable systems

Claude Froeschlé; Massimiliano Guzzo; Elena Lega

doi:10.3934/dcdsb.2005.5.687

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2005, Volume 5, Issue 3: 687-698. Doi: 10.3934/dcdsb.2005.5.687

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

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

Received: June 30, 2004

Revised: November 30, 2004

Published: July 2005

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Abstract

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, 70K43.

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