3-dimensional Anosov flows: Stable Manifolds and Foliations

This lecture explores the stability properties of 3-dimensional Anosov flows, focusing on the Hölder continuity of the splitting of the tangent space. It covers the non-smoothness of hyperbolic splitting, stable and unstable manifolds, invariant foliations, and the concept of Bowen's bracket. The lecture delves into the construction of rectangles as submanifolds and their parametrization, as well as the Markov property and the existence of a finite set of rectangles covering the manifold. The discussion extends to the distinction between Markov and non-Markov situations in the context of Anosov flows.