The Hausdorff dimension of the projections of self-affine carpets

Ferguson, Andrew and Jordan, Thomas and Shmerkin, Pablo (2009) The Hausdorff dimension of the projections of self-affine carpets. [MIMS Preprint]

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Abstract

We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if $\Lambda$ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of $\Lambda$ in a non-principal direction has Hausdorff dimension $\min(\gamma,1)$, where $\gamma$ is the Hausdorff dimension of $\Lambda$. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.

Item Type: MIMS Preprint
Uncontrolled Keywords: CICADA, self-affine sets, self-affine carpets, Hausdorff dimension, orthogonal projections
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 28 Measure and integration
Depositing User: Mr Pablo Shmerkin
Date Deposited: 14 Oct 2009
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1334

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