Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911370297999360 |
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| author | van Golden, S. Kalle, C. Kombrink, S. Samuel, T. |
| author_facet | van Golden, S. Kalle, C. Kombrink, S. Samuel, T. |
| contents | For countably infinite IFSs on $\mathbb R^2$ consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed Lüroth expansions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_10749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions van Golden, S. Kalle, C. Kombrink, S. Samuel, T. Dynamical Systems Metric Geometry Number Theory 28A80, 11A67, 11K55 For countably infinite IFSs on $\mathbb R^2$ consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed Lüroth expansions. |
| title | Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions |
| topic | Dynamical Systems Metric Geometry Number Theory 28A80, 11A67, 11K55 |
| url | https://arxiv.org/abs/2404.10749 |