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Surfaces of section for geodesic flows of closed surfaces
- Publication Year :
- 2022
-
Abstract
- We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $\Sigma$ 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 $\partial\Sigma$ as limit sets of the orbits of the geodesic flow that do not return to $\Sigma$. 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 Grayson's curve shortening flow.<br />Comment: 32 pages, 11 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2204.11977
- Document Type :
- Working Paper