论文标题
较高等级晶格对树突的结构
The structures of higher rank lattice actions on dendrites
论文作者
论文摘要
让$γ$成为一个更高的等级晶格，该晶格是在没有无限订单点的非重型树突上的$ x $。我们表明，存在一个非等级的子开发税$ y $，即$γ$ - invariant，并满足以下项目： (1) There is an inverse system of finite actions $\{(Y_i, Γ):i=1,2,3,\cdots\}$ with monotone bonding maps $ϕ_i: Y_{i+1}\rightarrow Y_i$ and with each $Y_i$ being a dendrite, such that $(Y, Γ|Y)$ is topologically conjugate to the inverse limit $（\ underset {\ longleftarrow} {\ lim}（y_i，γ），γ）$。 （2）第一个点映射$ r：x \ rightarrow y $是$（x，γ）$到$（y，γ| y）$的因子映射；如果$ x \ in x \ setminus y $，则$ r（x）$是无限轨道的$ y $的终点；对于每个$ y \ in y $，$ r^{ - 1}（y）$都是违约的，也就是说，有一个序列$ g_i \ inγ$，带有$ {\ rm diam}（\ rm diam}（g_ir^{ - 1}（y）（y）（y））\ rightarrow 0 $。
Let $Γ$ be a higher rank lattice acting on a nondegenerate dendrite $X$ with no infinite order points. We show that there exists a nondegenerate subdendrite $Y$ which is $Γ$-invariant and satisfies the following items: (1) There is an inverse system of finite actions $\{(Y_i, Γ):i=1,2,3,\cdots\}$ with monotone bonding maps $ϕ_i: Y_{i+1}\rightarrow Y_i$ and with each $Y_i$ being a dendrite, such that $(Y, Γ|Y)$ is topologically conjugate to the inverse limit $(\underset{\longleftarrow}{\lim}(Y_i, Γ), Γ)$. (2) The first point map $r:X\rightarrow Y$ is a factor map from $(X, Γ)$ to $(Y, Γ|Y)$; if $x\in X\setminus Y$, then $r(x)$ is an end point of $Y$ with infinite orbit; for each $y\in Y$, $r^{-1}(y)$ is contractible, that is there is a sequence $g_i\in Γ$ with ${\rm diam}(g_ir^{-1}(y))\rightarrow 0$.
