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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Correlation dimension
for iterated function systems


Authors: Wai Chin, Brian Hunt and James A. Yorke
Journal: Trans. Amer. Math. Soc. 349 (1997), 1783-1796
MSC (1991): Primary 28D20, 28D05; Secondary 60G18
MathSciNet review: 1407698
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Abstract: The correlation dimension of an attractor is a fundamental dynamical invariant that can be computed from a time series. We show that the correlation dimension of the attractor of a class of iterated function systems in $\mathbf {R}^N$ is typically uniquely determined by the contraction rates of the maps which make up the system. When the contraction rates are uniform in each direction, our results imply that for a corresponding class of deterministic systems the information dimension of the attractor is typically equal to its Lyapunov dimension, as conjected by Kaplan and Yorke.


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Additional Information

Wai Chin
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523 (On leave at: Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455)
Email: chin@ima.umn.edu

Brian Hunt
Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
Email: bhunt@ipst.umd.edu

James A. Yorke
Email: yorke@ipst.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01900-4
PII: S 0002-9947(97)01900-4
Received by editor(s): June 30, 1995
Article copyright: © Copyright 1997 American Mathematical Society