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The Hausdorff dimension of the projections of self-affine carpets

Tom 209 / 2010

Fundamenta Mathematicae 209 (2010), 193-213 MSC: Primary 28A80, 28A78. DOI: 10.4064/fm209-3-1

Streszczenie

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 ${\mit\Lambda}$ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of ${\mit\Lambda}$ in a non-principal direction has Hausdorff dimension $\min (\gamma ,1)$, where $\gamma$ is the Hausdorff dimension of ${\mit\Lambda}$. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.

Autorzy

• Andrew FergusonMathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL, UK
e-mail
• Thomas JordanDepartment of Mathematics
University of Bristol
University Walk, Clifton
Bristol BS8 1TW, UK
e-mail
• Pablo ShmerkinSchool of Mathematics
and Centre for Interdisciplinary Computational
and Dynamical Analysis
Alan Turing Building
University of Manchester
Oxford Road, Manchester M13 9PL, UK
e-mail

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