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Correlation Exponent

A measure $\nu$ of a Strange Attractor which allows the presence of Chaos to be distinguished from random noise. It is related to the Capacity Dimension $D$ and Information Dimension $\sigma$, satisfying

\nu\leq\sigma\leq D.
\end{displaymath} (1)

It satisfies
\nu\leq D_{\rm KY},
\end{displaymath} (2)

where $D_{\rm KY}$ is the Kaplan-Yorke Dimension. As the cell size goes to zero,
\lim_{\epsilon\to 0}\nu\to D_2,
\end{displaymath} (3)

where $D_2$ is the Correlation Dimension.


Grassberger, P. and Procaccia, I. ``Measuring the Strangeness of Strange Attractors.'' Physica D 9, 189-208, 1983.

© 1996-9 Eric W. Weisstein