Inhomogeneous self-similar sets and box dimensions
Volume 213 / 2012
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.
