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Kaplan-Yorke Dimension


 D_(KY)=j+(sigma_1+...+sigma_j)/(|sigma_(j+1)|),
(1)

where sigma_1<=sigma_n are Lyapunov characteristic exponents and j is the largest integer for which

 lambda_1+...+lambda_j>=0.
(2)

If nu=sigma=D, where nu is the correlation exponent, sigma the information dimension, and D the Hausdorff dimension, then

 D<=D_(KY)
(3)

(Grassberger and Procaccia 1983).


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References

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

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Kaplan-Yorke Dimension

Cite this as:

Weisstein, Eric W. "Kaplan-Yorke Dimension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kaplan-YorkeDimension.html

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