On the connection between the Nekhoroshev theorem and Arnold Diffusion

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. (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 $||R_{opt}||\propto \exp (1/{\epsilon }^{0.21})$ in the range $10^{-4}\le \epsilon \le 10^{-2}$. A comparison is made with the numerical results of Lega et al. (2003) in the same model.

Accepted in Celestial Mechanics and Dynamical Astronomy

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