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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Assouad dimension of self-affine carpets


Author: John M. Mackay
Journal: Conform. Geom. Dyn. 15 (2011), 177-187
MSC (2010): Primary 28A78; Secondary 28A80, 37F35
Published electronically: November 2, 2011
MathSciNet review: 2846307
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Abstract: We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.


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Additional Information

John M. Mackay
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Address at time of publication: Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom
Email: john.mackay@maths.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S1088-4173-2011-00232-3
PII: S 1088-4173(2011)00232-3
Keywords: Assouad dimension, conformal Assouad dimension, Bedford-McMullen carpets
Received by editor(s): July 23, 2010
Published electronically: November 2, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.