论文标题
在非阳性曲率中，封闭的大地测量学周围的时间波动平均
Fluctuations of time averages around closed geodesics in non-positive curvature
论文作者
论文摘要
我们考虑一个等级的测量流量一个非阳性曲率闭合歧管。我们证明了中央限制定理的渐近版本，用于从常规的封闭地球学构建的措施家族，从而收敛到Bowen-Margulis-knieper最大熵的度量。该技术扩展了Denker，Senti和Zhang的思想，他们证明了这种类型的渐近Lindeberg Central Limit lim lim lim lim lim lim lim limem on Praceic轨道定理，用于宽敞的地图，并具有规格属性。我们将这些技术从统一扩展到非均匀设置，从离散时间到连续时间。我们认为仅受林德堡条件和较弱的正方差条件约束的Hölder可观察结果。如果我们假设自然增强的正方差条件，则始终满足Lindeberg条件。我们的结果扩展到Hölder可观察物的动态阵列，并扩展到加权的周期性轨道度量，这些测量趋于融合到独特的平衡状态。
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.
