Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am interested in the relationship between non-linear differential equations and the Hausdorff, or fractal, dimension of the set of solutions.

For example, the Lorenz Attractor, which is a standard example in the theory of dynamical systems, apparently has a "correlation dimension" of 2.05, whatever that means. According to the authors who derived this result, the correlation dimension "is closely related to the fractal dimension and the information dimension, but its computation is considerably easier."

What I really want is the following: does anyone know of a system of coupled differential equations, preferably with smooth coefficients, for which a non-integer Hausdorff dimension of the solution set can be derived in an elegant way?


share|improve this question
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.