More Dynamics on Quotients of the Hyperbolic Plane
We continue the study of actions on locally homogeneous spaces by developing more of the dynamics of the modular surface. We prove ergodicity of the horocycle flow, and go on to deduce from mixing of the geodesic flow a form of unique ergodicity for the horocycle flow. We use this, together with the ergodic decomposition, to establish equidistribution for orbits of the horocycle flow.
KeywordsPeriodic Orbit Invariant Measure Unitary Representation Haar Measure Fundamental Domain
Unable to display preview. Download preview PDF.