Malo Jézéquel (CNRS, LMBA-Brest)
To an Anosov flow (i.e. a smooth uniformly hyperbolic flow on a closed manifold), one may associate a zeta function. This is a meromorphic function defined in term of the periodic orbits of the flow, that can be used for instance to count these orbits. After recalling this definition, I will explain how to extend it to certain “smooth pseudo-Anosov flows” on 3-manifolds, a class of flows that looks like Anosov flows except for a finite number of singular orbits. The motivation for studying zeta functions for these flows comes from topology. In particular, I will discuss a version of Fried’s conjecture for smooth pseudo-Anosov flows. This is a joint work with Jonathan Zung.