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Science 22 September 2000:
Vol. 289. no. 5487, pp. 2108 - 2110
DOI: 10.1126/science.289.5487.2108
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Reports

Graphical Evolution of the Arnold Web: From Order to Chaos

Claude Froeschlé, Massimiliano Guzzo,* Elena Lega

We represent graphically the evolution of the set of resonances of a quasi-integrable dynamical system, the so-called Arnold web, whose structure is crucial for the stability properties of the system. The basis of our representation is the use of an original numerical method, whose definition is directly related to the dynamics of orbits, and the careful choice of a model system. We also show the transition from the Nekhoroshev stability regime to the Chirikov diffusive one, which is a generic nontrivial phenomenon occurring in many physical processes, such as slow chaotic transport in the asteroid belt and beam-beam interaction.

Observatoire de Nice, Boulevard de l'Observatoire, Boîte Postale 4229, 06304 Nice Cedex 4, France.
*   Present address: Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Belzoni 7, 35131 Padova, Italy.

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Science. ISSN 0036-8075 (print), 1095-9203 (online)