Fifty years of the Erdős similarity conjecture
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916546503245824 |
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| author | Jung, Yeonwook Lai, Chun-Kit Mooroogen, Yuveshen |
| author_facet | Jung, Yeonwook Lai, Chun-Kit Mooroogen, Yuveshen |
| contents | Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickness and Hausdorff dimension zero. In this article, written after 50 years of the conjecture being proposed, we review progress on some new variants of the original problem: namely, the bi-Lipschitz variant, the topological variant, and a variant ``in the large''. These problems were recently studied by the authors and their collaborators. Each of them offers new perspectives on the original conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fifty years of the Erdős similarity conjecture Jung, Yeonwook Lai, Chun-Kit Mooroogen, Yuveshen Classical Analysis and ODEs Metric Geometry Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickness and Hausdorff dimension zero. In this article, written after 50 years of the conjecture being proposed, we review progress on some new variants of the original problem: namely, the bi-Lipschitz variant, the topological variant, and a variant ``in the large''. These problems were recently studied by the authors and their collaborators. Each of them offers new perspectives on the original conjecture. |
| title | Fifty years of the Erdős similarity conjecture |
| topic | Classical Analysis and ODEs Metric Geometry |
| url | https://arxiv.org/abs/2412.11062 |