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. (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.