# Assouad dimension of planar self-affine sets

## TL;DR

This paper computes the Assouad dimension of certain planar self-affine sets, demonstrating their minimality for conformal Assouad dimension and revealing strong tangential regularity properties.

## Contribution

It provides explicit calculation of Assouad dimension for self-affine sets under specific conditions and establishes their tangential regularity and minimality properties.

## Key findings

- Assouad dimension of the sets is explicitly calculated.
- Sets are minimal for conformal Assouad dimension.
- Any two generic points share the same tangent 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.

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Source: https://tomesphere.com/paper/1906.11007