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The Hausdorff dimension of the projections of self-affine carpets
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Ferguson, Andrew, Jordan, Thomas and Shmerkin, Pablo (2010) The Hausdorff dimension of the projections of self-affine carpets. Fundamenta Mathematicae, Vol.209 (No.3). pp. 193-213. doi:10.4064/fm209-3-1 ISSN 0016-2736.
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Official URL: http://dx.doi.org/10.4064/fm209-3-1
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: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Fundamenta Mathematicae | ||||
| Publisher: | Polska Akademia Nauk | ||||
| ISSN: | 0016-2736 | ||||
| Official Date: | 2010 | ||||
| Dates: |
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| Volume: | Vol.209 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 21 | ||||
| Page Range: | pp. 193-213 | ||||
| DOI: | 10.4064/fm209-3-1 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Manchester | ||||
| Grant number: | EP/E050441/1 (EPSRC) |
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