The Hausdorff Dimension of the Projections of Self-affine Carpets
نویسندگان
چکیده
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.
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