Collapsed Anosov Flows - Lecture 1: Basic Definitions and Main Results

Explore the concept of collapsed Anosov flows in this first lecture of a mini-course on partially hyperbolic systems. Delve into basic definitions and the characterization of collapsed Anosov flows, including stronger variants. Examine examples and key results in this field. Gain insights into the significance of collapsed Anosov flows for classifying partially hyperbolic diffeomorphisms in three-dimensional manifolds and their potential for studying finer dynamical properties. Learn how this class represents both a goal for classification and a framework for investigating dynamical attributes such as accessibility and ergodicity. Understand the connection between collapsed Anosov flows and self-orbit equivalences of Anosov flows, providing direction for discovering new examples in this category.

Thomas Barthelmé / Sérgio Fenley (Queen’s University / Florida State University), lecture 1