Assouad type dimensions and homogeneity of fractals

Jonathan M. Fraser

doi:10.1090/S0002-9947-2014-06202-8

Assouad type dimensions and homogeneity of fractals

Jonathan M. Fraser^*

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	6687-6733
Number of pages	47
Journal	Transactions of the American Mathematical Society
Volume	366
Issue number	12
Early online date	13 May 2014
DOIs	https://doi.org/10.1090/S0002-9947-2014-06202-8
Publication status	Published - Dec 2014

Keywords

Assouad dimension
Lower dimension
Self-affine carpet
Ahlfors regular
Measurability
Baire hierarchy
Self-similar sets
Hausdorff dimension
Packing dimension
Affine fractals
Spaces

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10.1090/S0002-9947-2014-06202-8

S0002-9947-2014-06202-8
© 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/)
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KW - Lower dimension

KW - Self-affine carpet

KW - Ahlfors regular

KW - Measurability

KW - Baire hierarchy

KW - Self-similar sets

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KW - Packing dimension

KW - Affine fractals

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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Assouad type dimensions and homogeneity of fractals

Abstract

Keywords

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