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Results tagged with fractals
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user 132466
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 iterations in the complex plane, or as strange attractors to continuous dynamical systems, (see Lorentz attractor).
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Why do weak and L metric topology for measures coincide?
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In Hutchinson's paper "Fractals and self similarity", it is claimed the following topology coincide on $M^1\cap\{\mu:\mu \mbox{ has compact suport}\}$:
The topology generated by taking as a sub-basis …
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Covering lemmas in Hochman's ''On self-similar sets with overlaps and inverse theorems for e...
I am confused about the covering lemmas in the captioned work and really hope to get some ideas here.
Firstly it is lemma 3.7. (Image of Lemma 3.7) (for convenience here is the lemma of this lemma (I …
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