Sub-Self-Similar Sets

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1995Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 347, page 3,121 (issn: 0002-9947,

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Authors: Falconer, K. J.;

doi: 10.2307/2154776 , 10.1090/s0002-9947-1995-1264809-x

Sub-Self-Similar Sets

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Abstract

A compact set E ⊆ R n E \subseteq {{\mathbf {R}}^n} is called sub-self-similar if E ⊆ ⋃ i = 1 m S i ( E ) E \subseteq \bigcup \nolimits _{i = 1}^m {{S_i}(E)} , where the S i {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.

Keywords

sub-self-similar sets, Fractals, Hausdorff and packing measures, box dimension, open set condition, Hausdorff dimension

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