Take the 2-minute tour ×  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
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