Assouad and lower dimensions of graph-directed Bedford-McMullen carpets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915031421026304 |
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| author | Qiu, Hua Wang, Qi Wang, Shufang |
| author_facet | Qiu, Hua Wang, Qi Wang, Shufang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_15407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Assouad and lower dimensions of graph-directed Bedford-McMullen carpets Qiu, Hua Wang, Qi Wang, Shufang Classical Analysis and ODEs 28A80 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. |
| title | Assouad and lower dimensions of graph-directed Bedford-McMullen carpets |
| topic | Classical Analysis and ODEs 28A80 |
| url | https://arxiv.org/abs/2411.15407 |