https://hal-ens-lyon.archives-ouvertes.fr/ensl-03816282Contreras, GonzaloGonzaloContrerasKnieper, GerhardGerhardKnieperMazzucchelli, MarcoMarcoMazzucchelliCNRS - Centre National de la Recherche ScientifiqueSchulz, Benjamin H.Benjamin H.SchulzSurfaces of section for geodesic flows of closed surfacesHAL CCSD2022[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Mazzucchelli, Marco2022-10-16 03:17:152022-10-17 03:09:332022-10-16 03:17:15enPreprints, Working Papers, ...1We 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.