Bounds on saddle connections for flat spheres
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915982233042944 |
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| author | Fu, Kai Tahar, Guillaume |
| author_facet | Fu, Kai Tahar, Guillaume |
| contents | We consider a flat metric with conical singularities on the sphere. Under the assumption that no partial sum of angle defects is equal to $2π$, we draw on the geometry of immersed disks to obtain an explicit upper bound on the number of saddle connections with at most $k$ self-intersections. Additionally, we establish an upper bound on their lengths for a surface with a normalized area. Finally, we apply these bounds to the counting of singular trajectories in irrational polygonal billiards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08940 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on saddle connections for flat spheres Fu, Kai Tahar, Guillaume Geometric Topology Differential Geometry We consider a flat metric with conical singularities on the sphere. Under the assumption that no partial sum of angle defects is equal to $2π$, we draw on the geometry of immersed disks to obtain an explicit upper bound on the number of saddle connections with at most $k$ self-intersections. Additionally, we establish an upper bound on their lengths for a surface with a normalized area. Finally, we apply these bounds to the counting of singular trajectories in irrational polygonal billiards. |
| title | Bounds on saddle connections for flat spheres |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2308.08940 |