We consider the geodesic flow for a rank one non-positive curvature closed manifold. We prove an asymptotic version of the Central Limit Theorem for families of measures constructed from regular closed geodesics converging to the Bowen-Margulis-Knieper measure of maximal entropy. The technique expands on ideas of Denker, Senti and Zhang, who proved this type of asymptotic Lindeberg Central Limit Theorem on periodic orbits for expansive maps with the specification property. We extend these techniques from the uniform to the non-uniform setting, and from discrete-time to continuous-time. We consider Hölder observables subject only to the Lindeberg condition and a weak positive variance condition. If we assume a natural strengthened positive variance condition, the Lindeberg condition is always satisfied. Our results extend to dynamical arrays of Hölder observables, and to weighted periodic orbit measures which converge to a unique equilibrium state.

我们考虑一阶非正曲率封闭流形的测地流。我们证明了中心极限定理的渐近形式，该定理适用于从规则的闭合测地线构造的测度系列，这些测度收敛到最大熵的Bowen-Margulis-Knieper测度。该技术扩展了Denker，Senti和Zhang的思想，他们证明了具有规范特性的膨胀图在周期轨道上的这种渐近Lindeberg中心极限定理。我们将这些技术从统一设置扩展到非统一设置，并从离散时间扩展到连续时间。我们认为Hölder观测值仅服从Lindeberg条件和弱正方差条件。如果我们假设一个自然加强的正方差条件，那么Lindeberg条件总是可以满足的。