Sub-self-similar sets

Falconer, K. J.

doi:10.1090/S0002-9947-1995-1264809-X

Sub-self-similar sets
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by K. J. Falconer PDF

Trans. Amer. Math. Soc. 347 (1995), 3121-3129 Request permission

Abstract:

A compact set $E \subseteq {{\mathbf {R}}^n}$ is called sub-self-similar if $E \subseteq \bigcup \nolimits _{i = 1}^m {{S_i}(E)}$, where the ${S_i}$ are similarity transfunctions. We consider various examples and constructions of such sets and obtain formulae for their Hausdorff and box dimensions, generalising those for self-similar sets.

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