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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-1,
author = {Andrew Ferguson and Thomas Jordan and Pablo Shmerkin},
title = {The Hausdorff dimension of the projections of self-affine carpets},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {193-213},
zbl = {1206.28011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-1}
}
Andrew Ferguson; Thomas Jordan; Pablo Shmerkin. The Hausdorff dimension of the projections of self-affine carpets. Fundamenta Mathematicae, Tome 209 (2010) pp. 193-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-1/