We obtain a qualitative characterization of the convergence rate of the averages (with respect to the Margulis measure) of C² functions over the iterations of domains in unstable manifolds of a topologically mixing C³ Anosov diffeomorphism with oriented invariant foliations. For this purpose, we extend the constructions of Margulis and Bufetov and introduce holonomy invariant families of finitely additive measures on unstable leaves and a Banach space in which holonomy invariant measures correspond to the (generalized) eigenfunctions of the transfer operator with biggest eigenvalues.

中文翻译：

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对阿诺索夫拟态不稳定叶片的有限加性测度

我们获得了C ²函数的平均值（相对于Margulis度量）的收敛速度的定性表征，这些C ²函数在具有定向不变叶面的拓扑混合C ³ Anosov微分形的不稳定流形中的域迭代上。为此，我们扩展了Margulis和Bufetov的构造，并介绍了不稳定叶子上有限可加测度的完整不变性族和Banach空间，其中完整不变性度量对应于具有最大特征值的传递算子的（广义）特征函数。