2016/12/16 by Mickaël Kourganoff, Kourganoff, Mickaël
Mathematics · Physics and Astronomy · #37D20 #37D50 #53D25 #70E55 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1612.05430
openalex publication_date 2016/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a billiard in the sphere S2 with circular obstacles, and give a sufficient condition for its flow to be uniformly hyperbolic. We show that the billiard flow in this case is approximated by an Anosov geodesic flow on a surface in the ambiant space S3. As an application, we show that every orientable surface of genus at least 11 admits an isometric embedding into S3 (equipped with the standard metric) such that its geodesic flow is Anosov. Finally, we explain why this construction cannot provide examples of isometric embeddings of surfaces in the Euclidean R3 with Anosov geodesic flows.