Assouad type dimensions and homogeneity of fractals
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- by Jonathan M. Fraser PDF
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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.References
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Additional Information
- Jonathan M. Fraser
- Affiliation: Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
- Address at time of publication: Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 946983
- Email: jmf32@st-andrews.ac.uk, jon.fraser32@gmail.com
- Received by editor(s): January 18, 2013
- Received by editor(s) in revised form: May 5, 2013
- Published electronically: May 13, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 6687-6733
- MSC (2010): Primary 28A80; Secondary 28A78, 28A20, 28C15
- DOI: https://doi.org/10.1090/S0002-9947-2014-06202-8
- MathSciNet review: 3267023