Shrinking rates of horizontal gaps for generic translation surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911062381559808 |
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| author | Chaika, Jon Fairchild, Samantha |
| author_facet | Chaika, Jon Fairchild, Samantha |
| contents | A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most $R$, we obtain precise decay rates as $R\to \infty$ for the difference in angle between two almost horizontal saddle connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03836 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Shrinking rates of horizontal gaps for generic translation surfaces Chaika, Jon Fairchild, Samantha Dynamical Systems Geometric Topology A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most $R$, we obtain precise decay rates as $R\to \infty$ for the difference in angle between two almost horizontal saddle connections. |
| title | Shrinking rates of horizontal gaps for generic translation surfaces |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2207.03836 |