论文标题
部分可观测时空混沌系统的无模型预测
Discrete two-generator subgroups of ${\rm PSL_2}$ over non-archimedean local fields
论文作者
论文摘要
令$ k $为一个非架构的本地字段，其特征性$ p $。我们为离散提供了两者子组的$ {\ rm psl_2}（k）$的必要条件，其中$ k = \ mathbb {q} _p $或$ g $都不包含订单$ p $的元素。我们给出了一种实用算法来决定这种亚组$ g $是否是离散的。我们还提供了实用算法来决定$ {\ rm sl_2}的两个生成子组（\ mathbb {r}）$还是$ {\ rm sl_2}（k）$（其中$ k $是$ \ mathbb {q} q} Q} _p $）的有限扩展。这项工作的关键要素是由$λ$树上作用于同位物的两产器组的结构定理。
Let $K$ be a non-archimedean local field with residue field of characteristic $p$. We give necessary and sufficient conditions for a two-generator subgroup $G$ of ${\rm PSL_2}(K)$ to be discrete, where either $K=\mathbb{Q}_p$ or $G$ contains no elements of order $p$. We give a practical algorithm to decide whether such a subgroup $G$ is discrete. We also give practical algorithms to decide whether a two-generator subgroup of either ${\rm SL_2}(\mathbb{R})$ or ${\rm SL_2}(K)$ (where $K$ is a finite extension of $\mathbb{Q}_p$) is dense. A crucial ingredient for this work is a structure theorem for two-generator groups acting by isometries on a $Λ$-tree.
