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

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 structur...

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Published in:Proceedings of the American Mathematical Society 2017-11, Vol.145 (11), p.4905-4918
Main Authors: FRASER, JONATHAN M., JORDAN, THOMAS
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B. ANALYSIS
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description 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.
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title The Assouad dimension of self-affine carpets with no grid structure
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