Kaplan-Yorke Dimension

$$D_{\rm KY}\equiv j+{\sigma_1+\ldots+\sigma_j\over \vert\sigma_{j+1}\vert},$$

where $\sigma_1\leq\sigma_n$ are Lyapunov Characteristic Exponents and $j$ is the largest Integer for which

$$\lambda_1+\ldots+\lambda_j\geq 0.$$

If $\nu=\sigma=D$, where $\nu$ is the Correlation Exponent, $\sigma$ the Information Dimension, and $D$ the Hausdorff Dimension, then

$$D\leq D_{\rm KY}$$

(Grassberger and Procaccia 1983).

References

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