Monday 04 Mar 2019: Dynamics Seminar: Periodic orbit growth on covers of Anosov flows
Richard Sharp - Warwick
It is well-known that the topological entropy of an Anosov flow on a compact manifold describes the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for periodic orbits of the lifted flow. This growth rate is bounded above by the original topological entropy but if the cover is infinite then the growth rate may be strictly smaller. In the important special case of a geodesic flow over a compact manifold with negative sectional curvatures, we have equality if and only if the cover is amenable. This result fails for general Anosov flows but we will discuss a recent result that gives a natural generalisation. This is joint work with Rhiannon Dougall.