The Hausdorff dimension of the projections of self-affine carpets

Details The Hausdorff dimension of the projections of self-affine carpets The Hausdorff dimension of the projections of self-affine carpets

2009-03-12

arxiv.org/abs/0903.2216v3

Mathematics

Dynamical Systems

20 pages. Some minor errors have been corrected and a few points have been clarified

Scientific paper

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

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