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

$$\nu\leq\sigma\leq D.$$ (1)

It satisfies

$$\nu\leq D_{\rm KY},$$ (2)

where $D_{\rm KY}$ is the Kaplan-Yorke Dimension. As the cell size goes to zero,

$$\lim_{\epsilon\to 0}\nu\to D_2,$$ (3)

where $D_2$ is the Correlation Dimension.

References

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