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

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Date
16/06/2017
Author
Fraser, Jonathan M.
Jordan, Thomas
Funder
The Leverhulme Trust
Grant ID
RF-2016-500
Keywords
Assouad dimension
Self-affine carpet
Local dimension
Bernoulli
QA Mathematics
T-NDAS
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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
DOI
https://doi.org/10.1090/proc/13629
ISSN
0002-9939
Type
Journal article
Rights
© 2017, 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 https://doi.org/10.1090/proc/13629
Description
JMF is financially supported by a Leverhulme Trust Research Fellowship.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/10061

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