Fractals deal with special sets that exhibit complicated patterns in every scale. Fractal sets usually have a Hausdorff dimension different from its topological dimension. Examples include Julia sets, the Sierpinski triangle, the Cantor set. Fractals naturally appear in dynamical system, such as ...
With this question I try to build up a systematization of different kinds of integrals. The following table differentiates between deterministic and stochastic integrals, the summation processes ...
Does anyone know of a good method for finding a lower bound of the Hausdorff dimension of a set $G$? The only method I could find is to find an $\alpha$-Hölder function $f \colon G \to H$ then ...
Does anyone know anything about self-similar (infinite) matrices, with more or less fractal(-like) structure and admitting meaningful matrix-algebra operations?