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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.04495 |
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| _version_ | 1866917691834499072 |
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| author | Berman, Jonah McAdam, Taylor Miller-Murthy, Ananth Uyanik, Caglar Wan, Hamilton |
| author_facet | Berman, Jonah McAdam, Taylor Miller-Murthy, Ananth Uyanik, Caglar Wan, Hamilton |
| contents | We explicitly compute the limiting slope gap distribution for saddle connections on any 2n-gon. Our calculations show that the slope gap distribution for a translation surface is not always unimodal, answering a question of Athreya. We also give linear lower and upper bounds for number of non-differentiability points as n grows. The latter result exhibits the first example of a non-trivial bound on an infinite family of translation surfaces and answers a question by Kumanduri-Sanchez-Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_04495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Slope Gap Distribution of Saddle Connections on the 2n-gon Berman, Jonah McAdam, Taylor Miller-Murthy, Ananth Uyanik, Caglar Wan, Hamilton Geometric Topology Dynamical Systems We explicitly compute the limiting slope gap distribution for saddle connections on any 2n-gon. Our calculations show that the slope gap distribution for a translation surface is not always unimodal, answering a question of Athreya. We also give linear lower and upper bounds for number of non-differentiability points as n grows. The latter result exhibits the first example of a non-trivial bound on an infinite family of translation surfaces and answers a question by Kumanduri-Sanchez-Wang. |
| title | Slope Gap Distribution of Saddle Connections on the 2n-gon |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2109.04495 |