The Hausdorff dimension of the projectionsof self-affine carpets

摘要

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