English

On the dimension of planar self-affine sets with non-invertible maps

Dynamical Systems 2023-08-02 v2

Abstract

In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition, the dimension equals to the affinity dimension for a typical choice of the linear parts of the non-invertible mappings, furthermore, we show that the dimension is strictly smaller than the affinity dimension for certain choices of parameters.

Keywords

Cite

@article{arxiv.2302.13037,
  title  = {On the dimension of planar self-affine sets with non-invertible maps},
  author = {Balázs Bárány and Viktor Körtvélyesi},
  journal= {arXiv preprint arXiv:2302.13037},
  year   = {2023}
}