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Mapping the Arnold web with a GPU-supercomputer

A. Seibert, S. Denisov, Alexey V. Ponomarev, P. Hanggi
Institute of Physics, University of Augsburg, Universitatstr. 1, D-86159 Augsburg, Germany
arXiv:1107.4107v1 [nlin.CD] (20 Jul 2011)

@article{2011arXiv1107.4107S,

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

   title={"{Mapping the Arnold web with a GPU-supercomputer}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1107.4107},

   primaryClass={"nlin.CD"},

   keywords={Nonlinear Sciences – Chaotic Dynamics, Physics – Computational Physics},

   year={2011},

   month={jul},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1107.4107S},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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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 $M geq 3$. 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.
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