English

Exceptional projections of self-affine sets: an introduction

Dynamical Systems 2025-03-11 v2 Classical Analysis and ODEs Metric Geometry

Abstract

We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image. We give a self-contained treatment of this bound and illustrate it through explicit examples, in the process exhibiting some smooth submanifolds of the Grassmannian which can be contained in the exceptional set in Marstrand's theorem.

Keywords

Cite

@article{arxiv.2308.04894,
  title  = {Exceptional projections of self-affine sets: an introduction},
  author = {Ian D. Morris},
  journal= {arXiv preprint arXiv:2308.04894},
  year   = {2025}
}

Comments

This expands and replaces an earlier manuscript. For submission to the proceedings of Fractals, Geometry and Stochastics VII