In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor, using Lyapunov exponents.
[1][2] By arranging the Lyapunov exponents in order from largest to smallest
λ
, let j be the largest 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.
[3] 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.