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Lyapunov Dimension

For a two-dimensional map with sigma_2>sigma_1,

d_(Lya)=1-(sigma_1)/(sigma_2),

where sigma_n are the Lyapunov characteristic exponents.

See also

Capacity Dimension, Kaplan-Yorke Conjecture

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References

Frederickson, P.; Kaplan, J. L.; Yorke, E. D.; and Yorke, J. A. "The Liapunov Dimension of Strange Attractors." J. Diff. Eq. 49, 185-207, 1983.Nayfeh, A. H. and Balachandran, B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. New York: Wiley, p. 549, 1995.

Referenced on Wolfram|Alpha

Lyapunov Dimension

Cite this as:

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

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