Graphical Evolution of the Arnold Web: From Order to Chaos

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Science  22 Sep 2000:
Vol. 289, Issue 5487, pp. 2108-2110
DOI: 10.1126/science.289.5487.2108

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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.

  • * Present address: Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Belzoni 7, 35131 Padova, Italy.

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