On The Lq dimensions of measures on Heuter-Lalley type self-affine sets

Jonathan M. Fraser, Tom Kempton

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study the Lq-dimensions of self-affine measures and the Käenmäki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, checkable conditions under which the Lq-dimensions are equal to the value predicted by Falconer for a range of q. As a corollary this gives a wider class of self-affine sets for which the Hausdorff dimension can be explicitly calculated. Our proof combines the potential theoretic approach developed by Hunt and Kaloshin with recent advances in the dynamics of self-affine sets.
Original languageEnglish
Pages (from-to)161-173
JournalProceedings of the American Mathematical Society
Volume146
Issue number1
Early online date1 Aug 2017
DOIs
Publication statusPublished - Jan 2018

Keywords

  • Self-affine set
  • Self-affine measure
  • Käenmäki measure
  • Lq-dimensions
  • Affinity dimension
  • Potential theoretic method

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