For many dynamical systems that are popular in applications, estimates are known for the decay of correlation in the case of Hölder continuous functions. In the present article, we suggest an approach that allows us to obtain estimates for correlation in dynamical systems in the case of arbitrary functions. This approach is based on approximation and estimates are obtained with the use of known estimates for Hölder continuous functions. We apply our approach to transitive Anosov diffeomorphisms and derive the central limit theorem for the characteristic functions of certain sets with boundary of zero measure.

中文翻译：

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动态系统中的相关性估计：从Hölder连续函数到一般可观测量

对于许多在应用中流行的动力学系统，在霍尔德连续函数的情况下，相关性的衰减是已知的。在本文中，我们建议一种方法，允许我们在任意函数的情况下获得动力学系统中相关性的估计。该方法基于近似值，并且使用已知的Hölder连续函数估计值获得估计值。我们将我们的方法应用于传递的Anosov微分形，并导出了零度量边界的某些集合的特征函数的中心极限定理。