Assouad dimension of planar self-affine sets
Dynamical Systems
2020-06-23 v2 Classical Analysis and ODEs
Metric Geometry
Abstract
We calculate the Assouad dimension of a planar self-affine set satisfying the strong separation condition and the projection condition and show that is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine set adheres to very strong tangential regularity by showing that any two points of , which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets.
Keywords
Cite
@article{arxiv.1906.11007,
title = {Assouad dimension of planar self-affine sets},
author = {Balázs Bárány and Antti Käenmäki and Eino Rossi},
journal= {arXiv preprint arXiv:1906.11007},
year = {2020}
}
Comments
25 pages, 2 figures; added Example 3.3, improved presentation