Assouad dimension of planar self-affine sets

Abstract

We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine set $X$ adheres to very strong tangential regularity by showing that any two points of $X$, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets.

25 pages, 2 figures; added Example 3.3, improved presentation