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Inhomogeneous self-similar sets and box dimensions

Name: Inhomogeneous self-similar sets and box dimensions
Creator: Fraser, Jonathan M.
Keywords: Covering regularity exponent, Box dimension, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, Inhomogeneous self-similar set, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Metric Geometry (math.MG), 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2012Embargo end date: 01 Jan 2013 United Kingdom English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Studia Mathematica, volume 213, pages 133-156 (issn: 0039-3223, eissn: 1730-6337,

Authors: Fraser, Jonathan M.;

doi: 10.4064/sm213-2-2 , 10.48550/arxiv.1301.1881

arXiv: http://arxiv.org/abs/1301.1881

Inhomogeneous self-similar sets and box dimensions

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Abstract

We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than the upper box dimension, Hausdorff dimension and packing dimension.

To appear in Studia Mathematica, 20 pages, 4 figures

Country

United Kingdom

Related Organizations

University of Salford
United Kingdom
University of St. Andrews
United Kingdom
Mathematical Institute
Czech Republic
UNIVERSITY OF ST ANDREWS
UNIVERSITY OF ST ANDREWS

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Keywords

Covering regularity exponent, Box dimension, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, Inhomogeneous self-similar set, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Metric Geometry (math.MG), 28A80, 26A18

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