The Hausdorff dimension of the projections of self-affine carpets
Volume 209 / 2010
Fundamenta Mathematicae 209 (2010), 193-213
MSC: Primary 28A80, 28A78.
DOI: 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 ${\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.
