Lyapunov Dimension

For a 2-D Map with $\sigma_2> \sigma_1$,

$$d_{\rm Lya} = 1-{\sigma_1\over\sigma_2},$$

where $\sigma_n$ are the Lyapunov Characteristic Exponents.

See also Capacity Dimension, Kaplan-Yorke Conjecture

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.