Assouad type dimensions and homogeneity of fractals

Fraser, Jonathan M.

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Date

12/2014

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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