Properties of a random Cantor set with overlaps
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917227656118272 |
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| author | Lai, Anna Chiara Loreti, Paola |
| author_facet | Lai, Anna Chiara Loreti, Paola |
| contents | We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set Condition fails. Our methodology is based on the theory of expansions in non-integer bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20644 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Properties of a random Cantor set with overlaps Lai, Anna Chiara Loreti, Paola Number Theory We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set Condition fails. Our methodology is based on the theory of expansions in non-integer bases. |
| title | Properties of a random Cantor set with overlaps |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.20644 |