Dimensions of an overlapping generalization of Baranski carpets

Pardo-Simon, Leticia (2019) Dimensions of an overlapping generalization of Baranski carpets. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 39 (3). pp. 733-763.

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Abstract

<jats:p>We determine the Hausdorff, the packing and the box-counting dimensions of a family of self-affine sets generalizing Barański carpets. More specifically, we fix a Barański system and allow both vertical and horizontal random translations, while preserving the structure of the rows and columns. The alignment kept in the construction allows us to give expressions for these fractal dimensions outside of a small set of exceptional translations. Such formulae will coincide with those for the non-overlapping case, and thus provide examples where the box-counting and the Hausdorff dimension do not necessarily agree. These results rely on Hochman’s recent work on the dimensions of self-similar sets and measures, and can be seen as an extension of Fraser and Shmerkin [On the dimensions of a family of overlapping self-affine carpets. <jats:italic>Ergod. Th. &amp; Dynam. Sys.</jats:italic><jats:uri xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://dx.doi.org/10.1017/etds.2015.21">doi: 10.1017/etds.2015.21</jats:uri>. Published online: 21 July 2015] results for Bedford–McMullen carpets with columns overlapping.</jats:p>

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	19 May 2017 07:27
Last Modified:	19 Jan 2023 07:04
DOI:	10.1017/etds.2017.57
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3007546