西奈-吕埃尔-鲍恩（SRB）测度的广义前推构造
A generalized push-forward construction of Sinai-Ruelle-Bowen measures
AI总结：
本文针对正体积集合上有效双曲的微分同胚，提出SRB测度构造中参考测度的广义选取方法，其结果还适用于均匀部分双曲或具主导分裂的微分同胚。
AI中文摘要：
对于Anosov微分同胚，构造西奈-吕埃尔-鲍恩（SRB）测度的几何方法是通过动力学将局部不稳定流形上的叶体积或任何与叶体积等价的测度向前推进，这类测度被称为参考测度。在应用中，人们常需使用相对于叶体积绝对连续的参考测度。本文证明，参考测度可从更广泛的一类测度中选取，这类测度是叶体积在局部不稳定流形上任意正叶体积的可测子集上的限制。此外，本文在更一般的情形下完成该推导，该情形针对在正体积集合上有效双曲的微分同胚；这类微分同胚由Climenhaga、Dolgopyat和Pesin在文献[\textcite{CDP}]中引入，他们当时已用几何方法构造了SRB测度。本文结果也适用于均匀部分双曲或更一般地拥有主导分裂的微分同胚。
英文摘要：
For Anosov diffeomorphisms the geometric approach for constructing Sinai-Ruelle-Bowen (SRB) measures works by pushing forward under the dynamics the leaf volume on a local unstable manifold or any measure that is equivalent to the leaf volume. Such a measure is called a reference measure. In applications one often needs to use a reference measure that is absolutely continuous with respect to leaf volume. In this paper we show that a reference measure can be chosen from a substantially more general class of measures which are the restriction of the leaf volume to any measurable subset of a local unstable manifold of positive leaf volume. Moreover, we do this in a more general settings of diffeomorphisms which are effectively hyperbolic on a set of positive volume. Such diffeomorphisms were introduced by Climenhaga, Dolgopyat and Pesin in \cite{CDP} where they used the geometric approach to construct SRB measures. Our results applies also to diffeomorphisms that are uniformly partially hyperbolic or more generally possess a dominated splitting.
