Let G be a connected, real linear, semisimple Lie group without compact factors and Γ < G a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on ΓG. 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 ΓG 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.

设G是一个连通的、实线性的、半单李群，没有紧因子，并且 Γ < G是一个 Zariski 稠密、离散子群。我们研究了 Γ G上正对角流的拓扑动力学。我们将 Hopf 坐标扩展到G的 Bruhat-Hopf 坐标，这给出了估计大型通用斜向元素乘积的椭圆部分的框架。通过将 Guivarc'h-Raugi 的结果重写为 Bruhat-Hopf 坐标，我们将混合规则 Weyl 室流的非游走集的Γ G中的原像划分为有限多个动态共轭子集。我们证明了拓扑混合的一个必要条件，并且当嘉当子群的中心化子恒等式的连通分量是阿贝尔时，我们证明它是充分的。