The Lyapunov dimension is a dimension estimate associated with the growth rates of infinitesimal perturbations in a dynamical system .
A common asymptotic convention uses the Kaplan-Yorke
dimension of the ordered Lyapunov
characteristic exponents . For a two-dimensional map with
Finite-time local versions instead apply the same interpolation to the logarithms of the singular values of the derivative of the
time map (Kuznetsov 2016). A local dimension computed in this way need not equal
the Hausdorff dimension of an invariant set .
See also Capacity Dimension ,
Eden's Conjecture ,
Kaplan-Yorke Conjecture ,
Kaplan-Yorke Dimension
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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. Kuznetsov, N. V. "The
Lyapunov Dimension and Its Estimation via the Leonov Method." Phys. Lett.
A 380 , 2142-2149, 2016. https://doi.org/10.1016/j.physleta.2016.04.036 . Nayfeh,
A. H. and Balachandran, B. Applied
Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Referenced on Wolfram|Alpha Lyapunov Dimension
Cite this as:
Weisstein, Eric W. "Lyapunov Dimension."
From MathWorld https://mathworld.wolfram.com/LyapunovDimension.html
Subject classifications
and 
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