Strong anomalous diffusion of the phase of a chaotic pendulum

Abstract

In this letter we consider the phase diffusion of a harmonically driven undamped pendulum and show that it is anomalous in the strong sense. The role played by the fractal properties of the phase space is highlighted, providing an illustration of the link between deterministic chaos and anomalous transport. Finally, we build a stochastic model which reproduces most properties of the original Hamiltonian system by alternating ballistic flights and random diffusion.

arXiv comment6 pages, 6 figures

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• Energy-dependent diffusion in a soft periodic Lorentz gas
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations