Mapping the Arnold web with a GPU-supercomputer

Abstract

The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M\ge 3$. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy shell. The Arnold diffusion is a slow process; consequently the mapping of the web presents a very time-consuming task. We demonstrate that the exploration of the Arnold web by use of a graphic processing unit (GPU)-supercomputer can result in distinct speedups of two orders of magnitude as compared to standard CPU-based simulations.

7 pages, 4 figures, a video supplementary provided at http://www.physik.uni-augsburg.de/~seiberar/arnold/Energy15_HD_frontNback.avi

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