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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

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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: 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:
DateEvent
2010Published
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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