Title: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 theclosing lemma for geodesic flows on Finsler surfaces.
Theclosing lemma says that for any compact smooth Finsler surface and any vector in the unit tangent bundle, the Finsler metric can be perturbed in topology so that 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 generic Finsler surface.