Conférencier: Thomas Barthelmé, Queen's University

An old problem in dynamical systems is to try to classify Anosov flows up to orbit-equivalence. This question is particularly interesting in dimension 3 where we both have lots of examples and a rich, but still poorly understood, relationships between the dynamics of the flow and the topology of the manifold. By a result of T. Barbot, classifying Anosov flows (or more general pseudo-Anosov flows) in dimension 3 up to orbit equivalence restricts to classifying, up to conjugacy, certain actions of \pi_1(M) on the orbit space, a topological plane with two transverse foliations.  In this talk, I will recall the above and discuss a new complete invariant for transitive (pseudo)-Anosov flows which often reduces to just knowing which conjugacy classes in \pi_1(M) are represented by periodic orbits of the flow. If time permits, I’ll talk about some applications with link to contact geometry. This is all joint work with Kathryn Mann, Steven Frankel and Sergio Fenley. 

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