3-dimensional Anosov flows: Mixing Properties and Equilibrium Measures

This lecture covers the dynamics of 3-dimensional Anosov flows, focusing on mixing properties and equilibrium measures. The instructor discusses topics such as topological mixing, joint integrability between stable and unstable foliations, and the Gibbs property of equilibrium states. Various theorems and examples are presented to illustrate the concepts, including the characterization of topological mixing and exponential mixing. The session concludes with a conjecture by Bowen-Ruelle regarding the exponential mixing behavior of Anosov flows for equilibrium measures. Overall, the lecture provides insights into the intricate dynamics of Anosov flows and their mixing properties.