Israel Journal of Mathematics

, Volume 16, Issue 2, pp 181–197

The central limit theorem for geodesic flows onn-dimensional manifolds of negative curvature

  • M. Ratner


In this paper we prove a central limit theorem for special flows built over shifts which satisfy a uniform mixing of type\(\gamma ^{n^\alpha } \), 0<γ<1, α>0. The function defining the special flow is assumed to be continuous with modulus of continuity of type\(f(z) = \sum\nolimits_{n = 0}^\infty {a_n z^n } \), 0<ρ<1, β>0, andd is the natural metric on sequence space. Geodesic flows on compact manifolds of negative curvature are isomorphic to special flows of this kind.


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Copyright information

© The Weizmann Science Press of Israel 1973

Authors and Affiliations

  • M. Ratner
    • 1
  1. 1.Institute of mathematicsThe Hebrew University of JerusalemJerusalemIsrael

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