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Mapping the Arnold web with a graphic processing unit

A. Seibert, S. Denisov, Alexey V. Ponomarev, P. Hanggi
Institute of Physics, University of Augsburg, Universitatstr.1, D-86159 Augsburg, Germany
Chaos 21, 043123, 2011

@article{seibert2011mapping,

   title={Mapping the Arnold web with a graphic processing unit},

   author={Seibert, A. and Denisov, S. and Ponomarev, AV and H{"a}nggi, P.},

   journal={CHAOS},

   volume={21},

   pages={043123},

   year={2011}

}

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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>=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-supercomputer can result in distinct speedups of two orders of magnitude as compared with standard CPU-based simulations.
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