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Critical behavior of a KAM surface: I. Empirical results

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Abstract

Kolmogorov-Arnol'd-Moser (KAM) surfaces are studied in the context of a perturbed two-dimensional twist map. In particular, we ask how a KAM surface can disappear as the perturbation parameter is increased. Following Greene, we use cycles to numerically construct the KAM curve and discover that at the critical coupling it shows structure at all length scales. Aspects of this structure are fitted by a scaling analysis; critical indices and scaling functions are determined numerically. Some evidence is presented which suggests that the results are universal.

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Authors and Affiliations

  1. The James Franck and Enrico Fermi Institutes of the University of Chicago, 5640 South Ellis Avenue, 60637, Chicago, Illinois

    Scott J. Shenker & Leo P. Kadanoff

Authors
  1. Scott J. Shenker
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  2. Leo P. Kadanoff
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Additional information

Supported in part by the Materials Research Laboratory Program of the National Science Foundation at the University of Chicago under grant No. NSF-MRL 7924007.

Robert R. McCormick and National Science Foundation Fellow

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Shenker, S.J., Kadanoff, L.P. Critical behavior of a KAM surface: I. Empirical results. J Stat Phys 27, 631–656 (1982). https://doi.org/10.1007/BF01013439

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