3D Anosov Flows: Exponential Mixing and Geometric Properties

This lecture by the instructor covers the exponential mixing of 3D Anosov flows, a class of dynamics exhibiting chaotic behavior. The lecture explains the geometric properties of Anosov flows, including the uniform hyperbolicity and partially hyperbolic dynamics. It also delves into the recent work solving the Bowen-Ruelle conjecture for 3D C Anosov flows. The presentation includes definitions, mixing properties, and approximation techniques, leading to a proof of exponential mixing. Examples such as geodesic flows on negatively curved surfaces are discussed to illustrate the concepts. The lecture emphasizes the structural stability of Anosov flows and the continuity of hyperbolic splitting.