**Title:** C^r closing lemma for geodesic flows on Finsler surfaces

**Speaker:** Dong Chen

**Speaker Info:** Ohio State University

**Brief Description:**

**Special Note**:

**Abstract:**

Title: C^r closing lemma for geodesic flows on Finsler surfacesAbstract: In this talk, I will give a proof of the C^r (r\geq 2) closing lemma for geodesic flows on Finsler surfaces. 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.

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.

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