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math.DG2022
Surfaces of section for geodesic flows of closed surfaces
Gonzalo Contreras, Gerhard Knieper, Marco Mazzucchelli +1
We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section that we constr…
math.DG2021★ 12 cited
Existence of Birkhoff sections for Kupka-Smale Reeb flows of closed contact 3-manifolds
Gonzalo Contreras, Marco Mazzucchelli
A Reeb vector field satisfies the Kupka-Smale condition when all its closed orbits are non-degenerate, and the stable and unstable manifolds of its hyperbolic closed orbits interse…
math.DG2003★ 3 cited
C2 densely the 2-sphere has an elliptic closed geodesic
Gonzalo Contreras, Fernando Oliveira
We prove that a riemannian metric on the 2-sphere or the projective plane can be C2-approximated by a smooth metric whose geodesic flow has an elliptic closed geodesic.