论文标题
Anosov同质空间上几何测量的奇异分解
Ergodic decompositions of geometric measures on Anosov homogeneous spaces
论文作者
论文摘要
对于最小的抛物线亚组$ p $，让$ g $为连接的半胶实元代数组和$ g $ $ g $的$γ$。让$ n $为$ p $的一能力的最大halosphical子组。我们描述了所有汉堡 - 罗布林措施的$ n $ ergodic分解，以及所有Bowen-Margulis-Sullivan措施$γ\ Backslash g $的$ er-ergodic分解。 As a consequence, we obtain the following refinement of the main result of [LO]: the space of all {\it non-trivial} $N$-invariant ergodic and $P^\circ$-quasi-invariant Radon measures on $Γ\backslash G$, up to constant multiples, is homeomorphic to ${\mathbb r}^{\ text {rank} \，g-1} \ times \ {1，\ cdots，k \} $，其中$ k $是$ p^\ circ $ -minimal子集的$γ\ backslash g $。
Let $G$ be a connected semisimple real algebraic group and $Γ$ a Zariski dense Anosov subgroup of $G$ with respect to a minimal parabolic subgroup $P$. Let $N$ be the maximal horospherical subgroup of $G$ given by the unipotent radical of $P$. We describe the $N$-ergodic decompositions of all Burger-Roblin measures as well as the $A$-ergodic decompositions of all Bowen-Margulis-Sullivan measures on $Γ\backslash G$. As a consequence, we obtain the following refinement of the main result of [LO]: the space of all {\it non-trivial} $N$-invariant ergodic and $P^\circ$-quasi-invariant Radon measures on $Γ\backslash G$, up to constant multiples, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}\times \{1, \cdots, k\}$ where $k$ is the number of $P^\circ$-minimal subsets in $Γ\backslash G$.
