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

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)4905-4918
Number of pages14
JournalProceedings of the American Mathematical Society
Issue number11
Early online date16 Jun 2017
DateAccepted/In press - 21 Dec 2016
DateE-pub ahead of print - 16 Jun 2017
DatePublished (current) - Nov 2017


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.

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