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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?


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