Surfaces of section for geodesic flows of closed surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915271525007360 |
|---|---|
| author | Contreras, Gonzalo Knieper, Gerhard Mazzucchelli, Marco Schulz, Benjamin H. |
| author_facet | Contreras, Gonzalo Knieper, Gerhard Mazzucchelli, Marco Schulz, Benjamin H. |
| contents | We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $Σ$ that we construct are either Birkhoff sections, meaning that they intersect every sufficiently long orbit segment of the geodesic flow, or at least they have some hyperbolic components in $\partialΣ$ as limit sets of the orbits of the geodesic flow that do not return to $Σ$. In order to prove these theorems, we provide a study of configurations of simple closed geodesics of closed orientable Riemannian surfaces, which may have independent interest. Our arguments are based on the curve shortening flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11977 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Surfaces of section for geodesic flows of closed surfaces Contreras, Gonzalo Knieper, Gerhard Mazzucchelli, Marco Schulz, Benjamin H. Differential Geometry Dynamical Systems Symplectic Geometry 53C22, 37D40, 53D25 We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $Σ$ that we construct are either Birkhoff sections, meaning that they intersect every sufficiently long orbit segment of the geodesic flow, or at least they have some hyperbolic components in $\partialΣ$ as limit sets of the orbits of the geodesic flow that do not return to $Σ$. In order to prove these theorems, we provide a study of configurations of simple closed geodesics of closed orientable Riemannian surfaces, which may have independent interest. Our arguments are based on the curve shortening flow. |
| title | Surfaces of section for geodesic flows of closed surfaces |
| topic | Differential Geometry Dynamical Systems Symplectic Geometry 53C22, 37D40, 53D25 |
| url | https://arxiv.org/abs/2204.11977 |