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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05935 |
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| _version_ | 1866914170415349760 |
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| author | Bashan, Sahar |
| author_facet | Bashan, Sahar |
| contents | We study the property of uniform discreteness within discrete orbits of non-uniform lattices in $SL_2(\mathbb{R})$, acting on $\mathbb{R}^2$ by linear transformations. We provide quantitative consequences of previous results by using Diophantine properties. We give a partial result toward a conjecture of Lelièvre regarding the set of long cylinder holonomy vectors of the "golden L" translation surface: for any $ε>0$, three points of this set can be found on a horizontal line within a distance of $ε$ of each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Non-Uniformly Discrete Orbits Bashan, Sahar Number Theory Dynamical Systems We study the property of uniform discreteness within discrete orbits of non-uniform lattices in $SL_2(\mathbb{R})$, acting on $\mathbb{R}^2$ by linear transformations. We provide quantitative consequences of previous results by using Diophantine properties. We give a partial result toward a conjecture of Lelièvre regarding the set of long cylinder holonomy vectors of the "golden L" translation surface: for any $ε>0$, three points of this set can be found on a horizontal line within a distance of $ε$ of each other. |
| title | On Non-Uniformly Discrete Orbits |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2409.05935 |