The Hausdorff dimension of the projections of self-affine carpets

AJ Ferguson, TM Jordan, P Shmerkin

Research output: Contribution to journalArticle (Academic Journal)peer-review

15 Citations (Scopus)

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 Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ,1), where γ is the Hausdorff dimension of Λ. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
Translated title of the contributionThe Hausdorff dimension of the projections of self-affine carpets
Original languageEnglish
Pages (from-to)193 - 213
Number of pages21
JournalFundamenta Mathematicae
Volume209, number 3
DOIs
Publication statusPublished - Sep 2010

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