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Israel Journal of Mathematics

, Volume 16, Issue 2, pp 181–197 | Cite as

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

  • M. Ratner
Article

Abstract

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.

Keywords

Central Limit Theorem Compact Manifold Gibbs Measure Negative Curvature Finite Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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