On the connection between the Nekhoroshev theorem and Arnold diffusion

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.