论文标题
局部一项不变的度量和限制一系列多项式轨迹在同质空间上的分布
Locally unipotent invariant measures and limit distribution of a sequence of polynomial trajectories on homogeneous spaces
论文作者
论文摘要
让$ g $为谎言组，$γ$是$ g $的格子。我们介绍了$ g/γ$的本地单位不变措施的概念。然后，我们证明，在某些条件下，$ g/γ$对多项式轨迹图像所支持的极限度量是本地单位不变的，因此为较高的多维多项式轨迹在同质空间上的高维多项式轨迹提供了部分答案，Shah在\ cite In \ cite in \ cite in \ cite中提高了一个均值。 证明依赖于Ratner的度量分类定理，对于奇异集合附近的多项式轨迹的线性化技术以及Shah的扭曲技术。
Let $G$ be a Lie group and $Γ$ be a lattice in $G$. We introduce the notion of locally unipotent invariant measures on $G/Γ$. We then prove that under some conditions, the limit measure supported on the image of polynomial trajectories on $G/Γ$ is locally unipotent invariant, thus give a partial answer to an equidistribution problem for higher dimensional polynomial trajectories on homogeneous spaces, which was raised by Shah in \cite{shah1994limit}. The proof relies on Ratner's measure classification theorem, linearization technique for polynomial trajectories near singular sets and a twisting technique of Shah.
