The Hausdorff dimension of the projections of self-affine carpets

Andrew Ferguson, Thomas Jordan, and Pablo Shmerkin. "The Hausdorff dimension of the projections of self-affine carpets." Fundamenta Mathematicae 209.3 (2010): 193-213. <http://eudml.org/doc/283113>.

@article{AndrewFerguson2010,
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.},
author = {Andrew Ferguson, Thomas Jordan, Pablo Shmerkin},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {3},
pages = {193-213},
title = {The Hausdorff dimension of the projections of self-affine carpets},
url = {http://eudml.org/doc/283113},
volume = {209},
year = {2010},
}

TY - JOUR
AU - Andrew Ferguson
AU - Thomas Jordan
AU - Pablo Shmerkin
TI - The Hausdorff dimension of the projections of self-affine carpets
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 3
SP - 193
EP - 213
AB - 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.
LA - eng
UR - http://eudml.org/doc/283113
ER -