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.