论文标题
部分可观测时空混沌系统的无模型预测
Rigidity for higher rank lattice actions on dendrites
论文作者
论文摘要
我们研究了Zimmer意义上对树突上更高等级的晶格动作的刚性，并表明：（1）如果$γ$是较高的等级晶格，而$ x $是一个无无限订单的非等级树突，那么任何$γ$在$ x $上的动作几乎是几乎免费的； （2）如果$γ$进一步是$ sl_n（\ Mathbb z）$的有限索引子组，$ n \ geq 3 $，则$ x $上的$γ$的每一个动作都有一个非平凡的几乎有限的子系统。在证明期间，我们通过其对树突的动作来了解有限生成的组的左定货性。
We study the rigidity in the sense of Zimmer for higher rank lattice actions on dendrites and show that: (1) if $Γ$ is a higher rank lattice and $X$ is a nondegenerate dendrite with no infinite order points, then any action of $Γ$ on $X$ cannot be almost free; (2) if $Γ$ is further a finite index subgroup of $SL_n(\mathbb Z)$ with $n\geq 3$, then every action of $Γ$ on $X$ has a nontrivial almost finite subsystem. During the proof, we get a new characterization of the left-orderability of a finitely generated group through its actions on dendrites.
