Using the factorization method of Eskin and Mirzakhani, we show that generalized u-Gibbs states over quantitatively non-integrable partially hyperbolic systems have absolutely continuous disintegrations on unstable manifolds. As an application, we show a pointwise equidistribution theorem analogous to the equidistribution results of Kleinbock–Shi–Weiss and Chaika–Eskin.

中文翻译：

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通过因式分解方法测量 Anosov 流的刚性

使用 Eskin 和 Mirzakhani 的因式分解方法，我们证明了定量不可积部分双曲系统上的广义u -Gibbs 态在不稳定流形上具有绝对连续的衰变。作为一个应用，我们展示了类似于 Kleinbock-Shi-Weiss 和 Chaika-Eskin 的均分布结果的逐点均分布定理。