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Assouad type dimensions and homogeneity of fractals

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S0002_9947_2014_06202_8.pdf (607.4Kb)
Date
12/2014
Author
Fraser, Jonathan M.
Keywords
Assouad dimension
Lower dimension
Self-affine carpet
Ahlfors regular
Measurability
Baire hierarchy
Self-similar sets
Hausdorff dimension
Packing dimension
Affine fractals
Spaces
QA Mathematics
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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 . https://doi.org/10.1090/S0002-9947-2014-06202-8
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1090/S0002-9947-2014-06202-8
ISSN
0002-9947
Type
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 Grant
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/5941

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