The Assouad dimension of self-affine carpets with no grid structure

Jonathan M. Fraser, Thomas Jordan

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urbański sets to the lower local dimensions of Bernoulli convolutions.
Original languageEnglish
Pages (from-to)4905-4918
JournalProceedings of the American Mathematical Society
Volume145
DOIs
Publication statusPublished - 16 Jun 2017

Keywords

  • Assouad dimension
  • Self-affine carpet
  • Local dimension
  • Bernoulli

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