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

Cited by in corpus (12)

• How to observe a non-Kerr spacetime
• Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective
• Kolmogorov and Nekhoroshev theory for the problem of three bodies
• Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river
• The speed of Arnold diffusion
• Scaling perspective on Intramolecular vibrational energy flow: analogies, insights, and challenges
• Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
• Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
• Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems
• New Hamiltonian expansions adapted to the Trojan problem
• Stochastic approach to diffusion inside the chaotic layer of a resonance
• Resonant normal form and asymptotic normal form behavior in magnetic bottle Hamiltonians