Dynamical Systems seminar - Comparison of entropy for infinite covering manifolds, and group extensions of subshifts of finite type

Dates

Wednesday, April 28, 2021 - 13:00 to 14:00

Speaker: Rhiannon Dougall (University of Bristol)

Title:  Comparison of entropy for infinite covering manifolds, and group extensions of subshifts of finite type. 

A classical example of an Anosov flow would be the geodesic flow associated to a compact hyperbolic manifold M. The periodic orbits are then closed geodesics in M, and this topic has a rich history. In general Anosov flows are not so well behaved, there may be infinitely many periodic orbits in a free homotopy class, in contract to geodesic flows. Nevertheless one has results on the asymptotic number of periodic orbits up to period T. In this talk we will discuss the problem of counting periodic orbits in infinite covering manifolds, where we relate the exponential growth rate of periodic orbits in the cover to properties of the covering group. Such results are rooted in analogous statements for group extensions of subshifts of finite type -- I will spend some time motivating this setting too. Featuring joint work with Richard Sharp.