Assouad type dimensions and homogeneity of fractals
Abstract
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.
Citation
Fraser , J M 2014 , ' Assouad type dimensions and homogeneity of fractals ' Transactions of the American Mathematical Society , vol 366 , no. 12 , pp. 6687-6733 . DOI: 10.1090/S0002-9947-2014-06202-8
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
ISSN
0002-9947Type
Journal article
Rights
© Copyright 2014 American Mathematical Society. First published in Transactions of the American Mathematical Society in Volume 366 (2014), published by the American Mathematical Society. This version may be reproduced under a CC-BY-NC-ND Creative Commons Licence (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Description
The author was supported by an EPSRC Doctoral Training GrantItems in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
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