Assouad dimension and fractal geometry
Abstract
This is a book to be published in 2020 by Cambridge University Press (Tracts in Mathematics Series). It focuses on the Assouad dimension of sets and measures in Euclidean space, as well as many variants on the Assouad dimension, including the lower dimension and Assouad spectrum. It considers these notions in the setting of fractal geometry and topics covered include: weak tangents, self-similar sets, self-affine sets, Mandelbrot percolation, limit sets of Kleinian groups, orthogonal projections, distance sets, and Kakeya sets. It also considers applications of these ideas to other areas, including: embedding theory, number theory, probability theory and functional analysis. It ends with a list of open problems.
Cite
@article{arxiv.2005.03763,
title = {Assouad dimension and fractal geometry},
author = {Jonathan M. Fraser},
journal= {arXiv preprint arXiv:2005.03763},
year = {2020}
}
Comments
Comments welcome. 292 pages, many figures. This material will be published by Cambridge University Press as Assouad Dimension and Fractal Geometry by Jonathan Fraser. This pre-publication version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. Copyright Jonathan Fraser 2020