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Effect of Islands in Diffusive Properties of the Standard Map for Large Parameter Values

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Abstract

In this paper we review, based on massive, long-term, numerical simulations, the effect of islands on the statistical properties of the standard map for large parameter values. Different sources of discrepancy with respect to typical diffusion are identified, and their individual roles are compared and explained in terms of available limit models.

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Acknowledgments

The authors were supported by Grants MTM2010-16425 (Spain) and 2009 SGR 67 (Catalonia). We thank Jaume Timoneda for maintaining the computing facilities of the Dynamical Systems Group of the Universitat de Barcelona, which were the main facilities used in this work, up to a total of floating point operations that exceeds 5 exaflop. The authors also want to thank Robert MacKay and Vered Rom-Kedar for helpful discussions on related topics.

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  1. Dept. de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Catalunya, Spain

    Narcís Miguel, Carles Simó & Arturo Vieiro

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  1. Narcís Miguel
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  2. Carles Simó
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  3. Arturo Vieiro
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Correspondence to Carles Simó.

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Communicated by Teresa Krick and James Renegar.

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Miguel, N., Simó, C. & Vieiro, A. Effect of Islands in Diffusive Properties of the Standard Map for Large Parameter Values. Found Comput Math 15, 89–123 (2015). https://doi.org/10.1007/s10208-014-9210-3

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  • DOI: https://doi.org/10.1007/s10208-014-9210-3

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