Vanessa Matus de la Parra, U of R
4:15 PM - 5:30 PM
One of the main interests in Dynamical Systems is to measure chaos. With this in mind, it makes sense to study the interaction of points in different regions of the space. Here is where the mixing comes up. A system is topologically mixing when it was the property of persistent interaction between independent regions of the space. In particular, this property implies that there is no prediction of the position of a point in the future. Showing that a flow on a compact metric space is topologically mixing is already a hard problem, but adding the non-compactness to our problem makes it even more challenging. A first step into this area is to study spaces where the dynamics in the non-compact zones is controlled. This is the case of hyperbolic surfaces, where the natural system to be considered is the flow defined by following the curves that minimize distance. We will do an overview on hyperbolic surfaces, their geodesic flow and their natural measure, and we will pass through the asymptotic independence of events (strong mixing) in order to conclude that the geodesic flow on hyperbolic Riemann surfaces of finite volume is topologically mixing.
Event contact: sliu72 at ur dot rochester dot edu