Pure Maths Colloquium: Rhiannon Dougall

“Hyperbolic dynamics” are defined by local expansion and contraction. These properties lead to “random looking” orbits, and indeed these systems satisfy various interesting statistical limit laws. Included in this class are some beautiful geometric examples such as the geodesic flow for a compact manifold of negative sectional curvatures. I will describe ways in which these dynamics capture some structure of the phase space. In particular, how dynamical growth characterises certain information about the fundamental group of the phase space and of the deck transformations given by coverings.