# Dynamical Systems Seminar-Geodesics and horocycles on a surface of constant negative curvature; the geodesic and horocycle flows.

**Title**: Geodesics and horocycles on a surface of constant negative curvature; the geodesic and horocycle flows.**Speaker:** Robbie Robinson & possibly some participants **Date and Time:** Friday, October 12, 9:00–10:00am**Place:** Rome 771

**Abstract:**The geodesic flow (for a compact hyperbolic surface) is an Anosov flow. In particular it has a Markov partition and positive topological entropy (so it is rather chaotic). The horocycle flow is minimal and uniquely ergodic. It has entropy zero (so not especially chaotic), yet is strongly mixing and even has Lebesgue spectrum. The geodesic and horocycle flows satisfy a famous commutation relation h^(s e^t) g^t = g^t h^s. Come find out what all this means (or at least I will begin to explain…to be continued later).