Fractal geometry of Bedford-McMullen carpets
Dynamical Systems
2020-08-25 v1 Classical Analysis and ODEs
Metric Geometry
Abstract
In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as \emph{Bedford-McMullen carpets}. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.
Keywords
Cite
@article{arxiv.2008.10555,
title = {Fractal geometry of Bedford-McMullen carpets},
author = {Jonathan M. Fraser},
journal= {arXiv preprint arXiv:2008.10555},
year = {2020}
}
Comments
21 pages, 3 figures. Survey article written for the Proceedings of the Fall 2019 Jean-Morlet Chair programme, Springer Lecture Notes Series