Critical Behavior of a KAM Surface: I. Empirical Results

TitleCritical Behavior of a KAM Surface: I. Empirical Results
Publication TypeJournal Article
Year of Publication1982
AuthorsKadanoff, L. P., & Shenker S.
Published inJournal of Physical Statistics
Volume27
Issue4
Page(s)631-656
Other Numbers3489
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.

Acknowledgment

This work is 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.

Bibliographic Notes

Journal of Physical Statistics, Vol. 27, Issue 4, pp. 631-656

Abbreviated Authors

L. P. Kadanoff and S. Shenker

ICSI Research Group

Networking and Security

ICSI Publication Type

Article in journal or magazine