Kaplan–Yorke conjecture


In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor, using Lyapunov exponents. By arranging the Lyapunov exponents in order from largest to smallest, let j be the index for which
and
Then the conjecture is that the dimension of the attractor is
This idea is used for the definition of the Lyapunov dimension.

Examples

Especially for chaotic systems, the Kaplan–Yorke conjecture is a useful tool in order to estimate the fractal dimension
and the Hausdorff dimension of the corresponding attractor.