Assouad type dimensions and homogeneity of fractals

Jonathan M. Fraser*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)

Abstract

We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.

Original languageEnglish
Pages (from-to)6687-6733
Number of pages47
JournalTransactions of the American Mathematical Society
Volume366
Issue number12
Early online date13 May 2014
DOIs
Publication statusPublished - Dec 2014

Keywords

  • Assouad dimension
  • Lower dimension
  • Self-affine carpet
  • Ahlfors regular
  • Measurability
  • Baire hierarchy
  • Self-similar sets
  • Hausdorff dimension
  • Packing dimension
  • Affine fractals
  • Spaces

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