Title: The specification property and its consequences for CAT(-1) spaces
Speaker: Dave Constantine (Wesleyan)
Abstract: The specification property is a strong dynamical property which allows one to find orbits in a system which obey quite robust sets of constraints. The canonical example of a flow with specification is the geodesic flow on a compact, negatively curved manifold. The CAT(-1) property is an attempt to capture the essential features of negative curvature in the metric space setting, without assumptions on the regularity of the space.
In this talk, covering joint work with Jean-Francois Lafont and Dan Thompson, I’ll prove that a weak form of the specification property holds for geodesic flows on compact, locally CAT(-1) geodesic metric spaces. I’ll discuss some of the dynamical consequences that follow from this property, and try to indicate how the CAT(-1) geometry of the spaces plays an essential role in the proof.