Geodesic Flow 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 9 in Ergodic Theory, 2011, pp 277-330 from Springer

Abstract: Abstract Having developed the language and basic technical toolbox of ergodic theory in earlier chapters, we begin our analysis of actions on locally homogeneous spaces by studying the geodesic flow on hyperbolic surfaces. Since we do not assume any prior knowledge of Lie theory or differential geometry, the material needed is introduced here. As an application, the geodesic flow is used to give another proof of ergodicity for the Gauss measure from Chapter 3.

Keywords: Invariant Measure; Haar Measure; Fundamental Domain; Discrete Subgroup; Hyperbolic Plane (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_9

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DOI: 10.1007/978-0-85729-021-2_9

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