The Hausdorff dimension of the projections of self-affine carpets

• Autorzy: Andrew Ferguson , Thomas Jordan , Pablo Shmerkin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 3
• Strony: 193-213

Daty

wydano

2010

Twórcy

autor

Andrew Ferguson

• Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK

autor

Thomas Jordan

• Department of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK

autor

Pablo Shmerkin

• School of Mathematics, and Centre for Interdisciplinary Computational, and Dynamical Analysis, Alan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, UK

Identyfikatory

DOI

10.4064/fm209-3-1