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More Dynamics on Quotients of the Hyperbolic Plane

In: Ergodic Theory

Author

Listed:
  • Manfred Einsiedler

    (ETH Zurich, Departement Mathematik)

  • Thomas Ward

    (University of East Anglia, School of Mathematics)

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.

Suggested Citation

  • Manfred Einsiedler & Thomas Ward, 2011. "More Dynamics on Quotients of the Hyperbolic Plane," Springer Books, in: Ergodic Theory, chapter 0, pages 347-402, Springer.
    • Handle: RePEc:spr:sprchp:978-0-85729-021-2_11
    DOI: 10.1007/978-0-85729-021-2_11
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