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arXiv · 0806.1703

On the connection between the Nekhoroshev theorem and Arnold Diffusion

C. Efthymiopoulos
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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 Froeschl\'{e} 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 $10^{-4}\leq\epsilon \leq 10^{-2}$. A comparison is made with the numerical results of Lega et al. (2003) in the same model.

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C. Efthymiopoulos. 2008-06-10. On the connection between the Nekhoroshev theorem and Arnold Diffusion. https://doi.org/10.1007/s10569-008-9151-8

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