The Assouad dimension of self-affine carpets with no grid structure
Classical Analysis and ODEs
2018-04-26 v2 Dynamical Systems
Number Theory
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.
Keywords
Cite
@article{arxiv.1607.02129,
title = {The Assouad dimension of self-affine carpets with no grid structure},
author = {Jonathan M. Fraser and Thomas Jordan},
journal= {arXiv preprint arXiv:1607.02129},
year = {2018}
}
Comments
14 pages, to appear in Proc. Amer. Math. Soc