On the connection between the Nekhoroshev theorem and Arnold Diffusion

Details On the connection between the Nekhoroshev theorem and Arnold Diffusion On the connection between the Nekhoroshev theorem and Arnold Diffusion

2008-06-10

arxiv.org/abs/0806.1703v1

Nonlinear Sciences

Chaotic Dynamics

Accepted in Celestial Mechanics and Dynamical Astronomy

Scientific paper

10.1007/s10569-008-9151-8

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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