Connection points on double regular polygons
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917902096007168 |
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| author | Boulanger, Julien |
| author_facet | Boulanger, Julien |
| contents | We study connection points on the double regular $n$-gon translation surface, for $n \geq 7$ odd and its staircase model. For $n \neq 9$, we provide a large family of points with coordinates in the trace field that are not connection points. This family includes the central points, and for $n=7$ we conjecture that all the remaining points are connection points. Further, in the case where $n \geq 7$ is a prime number, we provide a constructive proof by exhibiting an explicit separatrix passing through a central point that does not extend to a saddle connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connection points on double regular polygons Boulanger, Julien Geometric Topology Dynamical Systems Number Theory 51H99, 37C83, 11A55 We study connection points on the double regular $n$-gon translation surface, for $n \geq 7$ odd and its staircase model. For $n \neq 9$, we provide a large family of points with coordinates in the trace field that are not connection points. This family includes the central points, and for $n=7$ we conjecture that all the remaining points are connection points. Further, in the case where $n \geq 7$ is a prime number, we provide a constructive proof by exhibiting an explicit separatrix passing through a central point that does not extend to a saddle connection. |
| title | Connection points on double regular polygons |
| topic | Geometric Topology Dynamical Systems Number Theory 51H99, 37C83, 11A55 |
| url | https://arxiv.org/abs/2501.14657 |