Correlation Dimension for Iterated Function Systems

Wai Chin, Brian R. Hunt, and James A. Yorke

Trans. Amer. Math. Soc. 349 (1997), 1783--1796.

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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 {\bf 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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