Ergodic Theory pp 277-330 | Cite as

Geodesic Flow on Quotients of the Hyperbolic Plane


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.


Invariant Measure Haar Measure Fundamental Domain Discrete Subgroup Hyperbolic Plane 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Departement MathematikETH ZurichZurichSwitzerland
  2. 2.School of MathematicsUniversity of East AngliaNorwichUK

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