The Assouad dimension of self-affine carpets with no grid structure
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.
Citation
Fraser , J M & Jordan , T 2017 , ' The Assouad dimension of self-affine carpets with no grid structure ' , Proceedings of the American Mathematical Society , vol. 145 , pp. 4905-4918 . https://doi.org/10.1090/proc/13629
Publication
Proceedings of the American Mathematical Society
Status
Peer reviewed
ISSN
0002-9939Type
Journal article
Description
JMF is financially supported by a Leverhulme Trust Research Fellowship.Collections
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