A+ CATEGORY SCIENTIFIC UNIT

Inhomogeneous self-similar sets and box dimensions

Volume 213 / 2012

Jonathan M. Fraser Studia Mathematica 213 (2012), 133-156 MSC: Primary 28A80, 26A18. DOI: 10.4064/sm213-2-2

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 upper box dimension, Hausdorff dimension and packing dimension.

Authors

  • Jonathan M. FraserMathematical Institute
    University of St Andrews
    North Haugh
    St Andrews, Fife, KY16 9SS, Scotland
    e-mail

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