The Hausdorff dimension of the projections of self-affine carpets

Tom 209 / 2010

Andrew Ferguson, Thomas Jordan, Pablo Shmerkin Fundamenta Mathematicae 209 (2010), 193-213 MSC: Primary 28A80, 28A78. DOI: 10.4064/fm209-3-1

Streszczenie

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.

Autorzy

  • Andrew FergusonMathematics Institute
    Zeeman Building
    University of Warwick
    Coventry CV4 7AL, UK
    e-mail
  • Thomas JordanDepartment of Mathematics
    University of Bristol
    University Walk, Clifton
    Bristol BS8 1TW, UK
    e-mail
  • Pablo ShmerkinSchool of Mathematics
    and Centre for Interdisciplinary Computational
    and Dynamical Analysis
    Alan Turing Building
    University of Manchester
    Oxford Road, Manchester M13 9PL, UK
    e-mail

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