3:00–4:00 pm Eckhart Hall, Room 202
Anosov Fllows on 3-Manifolds
Anosov flows are a fascinating class of dynamical systems, generalizing and including geodesic flows on manifolds of negative curvature. These systems exhibit "local chaos but global stability" - individual orbits diverge wildly, but the systems as a whole are stable under perturbation. This stability means there is some hope to classify them by discrete algebraic invariants. Even on 3-dimensional spaces, this is an interesting and challenging problem. In this talk, I will describe some of the history and motivation for classification (dating back to work of Anosov and Smale in the 60s), connections with low-dimensional geometric topology, and will describe recent joint work with Barthelmé, Bowden, Frankel and Fenley (in various combinations) giving answering one thread of the classification problem in dimension 3.