Ferguson, Andrew and Jordan, Thomas and Shmerkin, Pablo (2009) The Hausdorff dimension of the projections of self-affine carpets. [MIMS Preprint]
![[thumbnail of projectionsrevised.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
projectionsrevised.pdf Download (283kB) |
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: | https://eprints.maths.manchester.ac.uk/id/eprint/1334 |
Actions (login required)
 |
View Item |