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Ergodic behaviour of Sullivan's geometric measure on a geometrically finite hyperbolic manifold

  • Daniel J. Rudolph (a1)
Abstract
Abstract

Sullivan's geometric measure on a geometrically finite hyperbolic manifold is shown to satisfy a mean ergodic theorem on horospheres and through this that the geodesic flow is Bernoulli.

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References
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[1]Ornstein D. S. & Weiss B.. Geodesic flows are Bernoullian. Isr. J. of Math. 14 (1973), 184198.
[2]Shields P.. Almost block independence. Z. Warsch. verw. Gebiete 49 (1979), 119123.
[3]Sullivan D.. Entropy, Hausdorf measures old and new, and limit sets of geometrically finite Kleinian groups. Ada Math. (1982).
[4]Ornstein D. S.. Ergodic Theory, Randomness and Dynamical Systems. Yale University Press: New Haven, 1974.
[5]Neumann J. von. Dynamical Systems of Continuous Spectra: Collected Works Vol. II, Pergamon Press; Oxford, 1961, 278286.
[6]McShane E.. Integration. Princeton University Press: Princeton, 1944.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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