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2009.70: The Hausdorff dimension of the projections of self-affine carpets

2009.70: Andrew Ferguson, Thomas Jordan and Pablo Shmerkin (2009) The Hausdorff dimension of the projections of self-affine carpets.

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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 2000 > 28 Measure and integration
MIMS number:2009.70
Deposited By:Mr Pablo Shmerkin
Deposited On:14 October 2009

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