论文标题
Anosov组：本地混合，计数和等分分配
Anosov groups: local mixing, counting, and equidistribution
论文作者
论文摘要
让$ g $成为一个连接的半神经真实代数组，相对于最小的抛物线子组，$γ<g $是zariski浓密的Anosov子组。我们描述了矩阵系数$ \ langle（\ exp TV）的渐近行为。 f_1，f_2 \ rangle $ in $ l^2（γ\ backslash g）$ as $ t \ to \ to \ to \ infty $对于任何$ f_1，f_2，f_2 \ in C_C（γ\ backslash g）$和任何$γ$的限制锥体内部的任何向量$ v $。这些渐进性涉及本文介绍的汉堡 - 罗布林措施的较高等级类似物。作为一个应用程序，对于$ g $的任何仿射对称亚组$ h $，我们就相应的$ g $的相应概括性cartan分解获得了$γ$ - 器的分配器计数结果。此外，我们获得了Duke-Rudnick-Sarnak和Eskin-McMullen的结果的类似物，以计算仿射对称空间中的离散$γ$ - 孔。
Let $G$ be a connected semisimple real algebraic group, and $Γ<G$ be a Zariski dense Anosov subgroup with respect to a minimal parabolic subgroup. We describe the asymptotic behavior of matrix coefficients $\langle (\exp tv). f_1, f_2\rangle$ in $L^2(Γ\backslash G)$ as $t\to \infty$ for any $f_1, f_2\in C_c(Γ\backslash G)$ and any vector $v$ in the interior of the limit cone of $Γ$. These asymptotics involve higher rank analogues of Burger-Roblin measures which are introduced in this paper. As an application, for any affine symmetric subgroup $H$ of $G$, we obtain a bisector counting result for $Γ$-orbits with respect to the corresponding generalized Cartan decomposition of $G$. Moreover, we obtain analogues of the results of Duke-Rudnick-Sarnak and Eskin-McMullen for counting discrete $Γ$-orbits in affine symmetric spaces $H\backslash G$.
