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On the connection between the Nekhoroshev theorem and Arnold diffusion

  • Christos Efthymiopoulos
Original Article

Abstract

The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschlé et al. (Science 289:2108–2110, 2000). A resonant normal form is constructed by a computer program and the size of its remainder ||R opt || at the optimal order of normalization is calculated as a function of the small parameter \({\epsilon}\) . We find that the diffusion coefficient scales as \({D \propto ||R_{opt}||^3}\) , while the size of the optimal remainder scales as \({||R_{opt}|| \propto {\rm exp}(1/\epsilon^{0.21})}\) in the range \({10^{-4} \leq \epsilon \leq 10^{-2}}\) . A comparison is made with the numerical results of Lega et al. (Physica D 182:179–187, 2003) in the same model.

Keywords

Normal forms Nekhoroshev theorem Arnold diffusion 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Research Center for Astronomy and Applied MathematicsAcademy of AthensAthensGreece

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