The Assouad dimension of self-affine carpets with no grid structure
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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.
Fraser , J M & Jordan , T 2016 , ' The Assouad dimension of self-affine carpets with no grid structure ' Proceedings of the American Mathematical Society .
Proceedings of the American Mathematical Society
© 2016, American Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.ams.org /
JMF is financially supported by a Leverhulme Trust Research Fellowship.
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