English

Non-invertible planar self-affine sets

Dynamical Systems 2024-11-27 v2

Abstract

We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamical formalism where, for dominated and irreducible matrices, we completely characterize the behavior of the pressures.

Keywords

Cite

@article{arxiv.2205.07351,
  title  = {Non-invertible planar self-affine sets},
  author = {Antti Käenmäki and Petteri Nissinen},
  journal= {arXiv preprint arXiv:2205.07351},
  year   = {2024}
}

Comments

17 pages

R2 v1 2026-06-24T11:17:54.374Z