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-Urba\'nski sets to the lower local dimensions of Bernoulli convolutions.
| Original language | English |
|---|---|
| Pages (from-to) | 4905-4918 |
| Number of pages | 14 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 145 |
| Issue number | 11 |
| Early online date | 16 Jun 2017 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
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Dr Thomas M Jordan
- Probability, Analysis and Dynamics
- School of Mathematics - Senior Lecturer in Pure Mathematics
- Pure Mathematics
- Ergodic theory and dynamical systems
Person: Academic , Member