Weakly separated self-affine carpets
Dynamical Systems
2026-05-12 v2
Abstract
In this paper, we study the Hausdorff and the box-counting dimensions of diagonally aligned self-affine carpets whose projections to the - and -axes satisfy the weak separation condition. In particular, we show that the Hausdorff dimension equals the limit of the Bara\'nski formula, and that the box-counting dimension is the limit of the Feng-Wang formula taken over the -fold compositions of the IFS. We also prove several equivalent formulas for the box-counting dimension, and derive the dimension values for two examples.
Cite
@article{arxiv.2506.06851,
title = {Weakly separated self-affine carpets},
author = {Balázs Bárány and Levente David},
journal= {arXiv preprint arXiv:2506.06851},
year = {2026}
}