论文标题
阳性对角线流的拓扑混合
Topological mixing of positive diagonal flows
论文作者
论文摘要
让$ g $为一个半简单的真实谎言组，没有紧凑的因素，而$γ<g $ a zariski密集，离散子组。我们研究了$γ\ Backslash g $上对角线流的拓扑动力学。我们将HOPF坐标扩展到$ g $的Bruhat-Hopf坐标，该框架为估算大型通用Loxodormic元素的椭圆形部分提供了框架。通过将Guivarc'h-Raugi的结果重写为Bruhat-Hopf坐标，我们将$γ\ Backslash g $的预先映射划分为一组非随机混合的常规Weyl室流，将其分为有限的许多动态结合的子集。我们证明了拓扑混合的必要条件，当cartan子组的中央器的身份的连接成分是Abelian时，我们证明这已经足够了。
Let $G$ be a semi-simple real Lie group without compact factors and $ Γ< G$ a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on $Γ\backslash G$. We extend Hopf coordinates to Bruhat-Hopf coordinates of $G$, which gives the framework to estimate the elliptic part of products of large generic loxodromic elements. By rewriting results of Guivarc'h-Raugi into Bruhat-Hopf coordinates, we partition the preimage in $Γ\backslash G$ of the non-wandering set of mixing regular Weyl chamber flows, into finitely many dynamically conjugated subsets. We prove a necessary condition for topological mixing, and when the connected component of the identity of the centralizer of the Cartan subgroup is abelian, we prove it is sufficient.
