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 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 ∂Σ 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 close… Show more
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