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

DOI:
https://doi.org/10.1090/S0002-9947-97-01900-4

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 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:
https://doi.org/10.1090/S0002-9947-97-01900-4

Received by editor(s):
June 30, 1995

Article copyright:
© Copyright 1997
American Mathematical Society