Abstract
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.
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© 2011 Springer-Verlag London Limited
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Einsiedler, M., Ward, T. (2011). More Dynamics on Quotients of the Hyperbolic Plane. In: Ergodic Theory., vol 259. Springer, London. https://doi.org/10.1007/978-0-85729-021-2_11
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DOI: https://doi.org/10.1007/978-0-85729-021-2_11
Publisher Name: Springer, London
Print ISBN: 978-0-85729-020-5
Online ISBN: 978-0-85729-021-2
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