Title: $C^r$ closing lemma for geodesic flows on Finsler surfaces
Speaker: Dong Chen (Ohio State University)
Abstract: A Finsler metric on a smooth manifold is a smooth family of quadratically convex norms on each tangent space. The geodesic flow on a Finsler manifold is a 2-homogeneous Lagrangian flow. In this talk, I will give a proof of the $C^r (r\geq 2)$ closing lemma for geodesic flows on Finsler surfaces.
The $C^r$ closing lemma says that for any compact smooth Finsler surface and any vector $v$ in the unit tangent bundle, the Finsler metric can be perturbed in $C^r$ topology so that $v$ is tangent to a periodic geodesic in the resulting metric. This allows us to get the density of periodic geodesics in the tangent bundle of a $C^r$ generic Finsler surface.
