标题： 高维测度在仿射不变子流形上的有效等分布 显示英文标题

标题： Effective equidistribution of large dimensional measures on affine invariant submanifolds

摘要： 不稳定叶层，局部上由改变周期坐标中的水平分量给出，在翻译曲面的研究中起着重要作用，包括它们的形变理论以及对环形不变测度的理解。 在本文中，我们证明了不稳定叶层上大维数的测度在仿射不变子流形中均匀分布，并给出了一个有效的速率。 在齐次动力系统设置中的类似结果被关键地用于Lindenstrauss-Mohammadi和Lindenstrauss--Mohammadi--Wang的有效密度和均匀分布结果中。 显示英文摘要

摘要： The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their deformation theory and in the understanding of horocycle invariant measures. In this article we show that measures of large dimension on the unstable foliation equidistribute in affine invariant submanifolds and give an effective rate. An analogous result in the setting of homogeneous dynamics is crucially used in the effective density and equidistribution results of Lindenstrauss-Mohammadi and Lindenstrauss--Mohammadi--Wang.