Zhiyuan Zhang (Imperial College)

Abstract: Exponential mixing of 3D Anosov flows

Abstract: Anosov flows are a generalization of geodesic flows on the unit tangent bundles of compact manifolds of negative sectional curvature. They are basic examples of hyperbolic (chaotic) dynamical systems. The study of quantitative asymptotic behaviors of Anosov flows provides interesting analytical problems. We will review some foundational results of Ruelle, Bowen, Pollicott, Dolgopyat, Liverani, etc. Then we will discuss in detail a result of Tsujii on generic exponential mixing of volume preserving 3D Anosov flow, and its generalization due to Tsujii and myself to all topological mixing smooth 3D Anosov flows. We will also mention some related open questions.