Weakly separated self-affine carpets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911665428103168 |
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| author | Bárány, Balázs David, Levente |
| author_facet | Bárány, Balázs David, Levente |
| contents | In this paper, we study the Hausdorff and the box-counting dimensions of diagonally aligned self-affine carpets whose projections to the $x$- and $y$-axes satisfy the weak separation condition. In particular, we show that the Hausdorff dimension equals the limit of the Barański formula, and that the box-counting dimension is the limit of the Feng-Wang formula taken over the $n$-fold compositions of the IFS. We also prove several equivalent formulas for the box-counting dimension, and derive the dimension values for two examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weakly separated self-affine carpets Bárány, Balázs David, Levente Dynamical Systems 28A80 28A78 In this paper, we study the Hausdorff and the box-counting dimensions of diagonally aligned self-affine carpets whose projections to the $x$- and $y$-axes satisfy the weak separation condition. In particular, we show that the Hausdorff dimension equals the limit of the Barański formula, and that the box-counting dimension is the limit of the Feng-Wang formula taken over the $n$-fold compositions of the IFS. We also prove several equivalent formulas for the box-counting dimension, and derive the dimension values for two examples. |
| title | Weakly separated self-affine carpets |
| topic | Dynamical Systems 28A80 28A78 |
| url | https://arxiv.org/abs/2506.06851 |