Mathematics Colloquia and Seminars

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Unlike the geodesic flow on surfaces of nonnegative curvature, the geodesic flow on hyperbolic surfaces is ergodic. On compact hyperbolic surfaces, the horocycle flow is ergodic as well. After briefly introducing the basics of two-dimensional hyperbolic geometry, I'll discuss the geodesic and horocycle flows and characterize geodesic and horocycle orbits.