More Dynamics on Quotients of the Hyperbolic Plane

Manfred Einsiedler () and Thomas Ward ()
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Manfred Einsiedler: ETH Zurich, Departement Mathematik
Thomas Ward: University of East Anglia, School of Mathematics

Chapter Chapter 11 in Ergodic Theory, 2011, pp 347-402 from Springer

Abstract: 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.

Keywords: Periodic Orbit; Invariant Measure; Unitary Representation; Haar Measure; Fundamental Domain (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-021-2_11

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DOI: 10.1007/978-0-85729-021-2_11

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