Assouad and lower dimensions of graph-directed Bedford-McMullen carpets
Classical Analysis and ODEs
2024-11-26 v1
Abstract
We calculate the Assouad and lower dimensions of graph-directed Bedford-McMullen carpets, which reflect the extreme local scaling laws of the sets, in contrasting with known results on Hausdorff and box dimensions. We also investigate the relationship between distinct dimensions. In particular, we identify an equivalent condition when the box and Assouad dimension coincide, and show that under this condition, the Hausdorff dimension attains the same value.
Keywords
Cite
@article{arxiv.2411.15407,
title = {Assouad and lower dimensions of graph-directed Bedford-McMullen carpets},
author = {Hua Qiu and Qi Wang and Shufang Wang},
journal= {arXiv preprint arXiv:2411.15407},
year = {2024}
}
Comments
24 pages, 6 figures