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Title of Journal: Celestial Mech Dyn Astr

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Abbravation: Celestial Mechanics and Dynamical Astronomy

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Kluwer Academic Publishers

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DOI

10.1002/andp.18280870411

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1572-9478

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Analysis of the Chaotic Behaviour of Orbits Diffus

Authors: Claude Froeschlé Elena Lega Massimiliano Guzzo
Publish Date: 2006/03/18
Volume: 95, Issue: 1-4, Pages: 141-153
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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 socalled 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

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