Sub-self-similar sets-Reference-Cited by-同舟云学术

Sub-self-similar sets

Published:1995 Issue:8 Volume:347 Page:3121-3129
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Falconer K. J.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1995-347-08/S0002-9947-1995-1264809-X/S0002-9947-1995-1264809-X.pdf

Reference12 articles.

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