论文标题
霍斯利克动作和Anosov组的不变措施
Invariant measures for horospherical actions and Anosov groups
论文作者
论文摘要
令$γ$为Zariski密集的Anosov子组，该子组是连接的半神经元代数组$ g $。对于$ g $的最大Halosphical子组$ n $ $ n $，我们表明，所有非平凡$ nm $ $ nm $ invariant ergodic的空间和$ a $ quasi-quasi-Invariant Radon对$γ\ backslash g $的radon radon措施，直至比例，直到$ a}其中$ a $是最大的真实分式圆环，而$ m $是最大的紧凑型亚组，它标准化了$ n $。主要成分之一是建立所有汉堡措施的$ nm $ ergodicity。
Let $Γ$ be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $Γ\backslash G$, up to proportionality, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$. One of the main ingredients is to establish the $NM$-ergodicity of all Burger-Roblin measures.
