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

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.