论文标题
Birkhoff上的精确渐近学总和用于动态系统
Precise asymptotics on the Birkhoff sums for dynamical systems
论文作者
论文摘要
我们在动态系统的Birkhoff总和上建立了两个确切的渐近结果。这些结果与先前由HSU和Robbins，Erdős，Heyde获得的自变和相同随机变量的算术和相同的随机变量的算术和相同。我们将结果应用于高斯地图，并在莱维定理中获得新的精确渐近学，这是在$（0,1）$中定期持续扩展非理性数字的持续分数。
We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These results are parallel to that on the arithmetic sums of independent and identically distributed random variables previously obtained by Hsu and Robbins, Erdős, Heyde. We apply our results to the Gauss map and obtain new precise asymptotics in the theorem of Lévy on the regular continued fraction expansion of irrational numbers in $(0,1)$.
