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Analysis of the chaotic behaviour of orbits diffusing along the Arnold web

  • Claude Froeschlé
  • Elena Lega
  • Massimiliano Guzzo
Conference paper

Abstract

In a previous work [Guzzo et al. DCDS B 5, 687–698 (2005)] we have provided numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We have shown 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. In the present work we study in more detail the chaotic behaviour of a set of 90 orbits which diffuse on the Arnold web. We find that the largest Lyapunov exponent does not seem to converge for the individual orbits while the mean Lyapunov exponent on the set of 90 orbits does converge. In other words, a kind of average mixing characterizes the diffusion. Moreover, the Local Lyapunov Characteristic Numbers (LLCNs), on individual orbits appear to reflect the different zones of the Arnold web revealed by the Fast Lyapunov Indicator. Finally, using the LLCNs we study the ergodicity of the chaotic part of the Arnold web.

Keywords

KAM and Nekhoroshev theorem Arnold’s diffusion Chaos detection 

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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Claude Froeschlé
    • 1
  • Elena Lega
    • 1
  • Massimiliano Guzzo
    • 2
  1. 1.Observatoire de la Côte d’AzurNice Cedex 4France
  2. 2.Dipartimento di Matematica pura e Applicata Università di PadovaPadovaItaly

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