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.
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Ratner, M. The central limit theorem for geodesic flows onn-dimensional manifolds of negative curvature. Israel J. Math. 16, 181–197 (1973). https://doi.org/10.1007/BF02757869
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DOI: https://doi.org/10.1007/BF02757869