Assouad type dimensions and homogeneity of fractals
Metric Geometry
2014-10-29 v1 Classical Analysis and ODEs
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, like 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.
Keywords
Cite
@article{arxiv.1301.2934,
title = {Assouad type dimensions and homogeneity of fractals},
author = {Jonathan M. Fraser},
journal= {arXiv preprint arXiv:1301.2934},
year = {2014}
}
Comments
40 pages, 6 figures