1Mathematics Institute Zeeman Building University of Warwick Coventry CV4 7AL, UK 2Department of Mathematics University of Bristol University Walk, Clifton Bristol BS8 1TW, UK 3School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis Alan Turing Building University of Manchester Oxford Road, Manchester M13 9PL, UK
Fundamenta Mathematicae, Tome 209 (2010) no. 3, pp. 193-213
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 ${\mit\Lambda} $ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of ${\mit\Lambda} $ in a non-principal direction has Hausdorff dimension $\min (\gamma ,1)$, where $\gamma $ is the Hausdorff dimension of ${\mit\Lambda} $. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
Keywords:
study orthogonal projections large class self affine carpets which contains carpets bedford mcmullen special cases main result mit lambda carpet certain natural irrationality conditions every orthogonal projection mit lambda non principal direction has hausdorff dimension min gamma where gamma hausdorff dimension mit lambda generalizes recent result peres shmerkin sums cantor sets
Affiliations des auteurs :
Andrew Ferguson
1
;
Thomas Jordan
2
;
Pablo Shmerkin
3
1
Mathematics Institute Zeeman Building University of Warwick Coventry CV4 7AL, UK
2
Department of Mathematics University of Bristol University Walk, Clifton Bristol BS8 1TW, UK
3
School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis Alan Turing Building University of Manchester Oxford Road, Manchester M13 9PL, UK
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Andrew Ferguson; Thomas Jordan; Pablo Shmerkin. The Hausdorff dimension of the projections
of self-affine carpets. Fundamenta Mathematicae, Tome 209 (2010) no. 3, pp. 193-213. doi: 10.4064/fm209-3-1
