Visible part of dominated self-affine sets in the plane

TL;DR

This paper investigates the Assouad dimension of the visible parts of self-affine sets in the plane, showing it equals 1 in most directions regardless of overlaps, under domination and projection conditions.

Contribution

It establishes that the Assouad dimension of the visible part is 1 outside limit directions, extending understanding of self-affine set visibility without overlap restrictions.

Findings

Assouad dimension of visible part equals 1 outside limit directions

Result holds regardless of cylinder overlaps

Sharpness of the dimension result is discussed

Abstract

The dimension of the visible part of self-affine sets, that satisfy domination and a projection condition, is being studied. The main result is that the assouad dimension of the visible part equals to 1 for all directions outside the set of limit directions of the cylinders of the self-affine set. The result holds regardless of the overlap of the cylinders. The sharpness of the result is also being discussed.