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 contribution | The Hausdorff dimension of the projections of self-affine carpets |
|---|---|
| Original language | English |
| Pages (from-to) | 193 - 213 |
| Number of pages | 21 |
| Journal | Fundamenta Mathematicae |
| Volume | 209, number 3 |
| DOIs | |
| Publication status | Published - Sep 2010 |