Mumford树图与离散p-adic对称
Mumford dendrograms and discrete p-adic symmetries
摘要：
在这篇文章中，我们提出了一个有效的编码树状图嵌入到布鲁哈特-山雀树与$p$ -进数域。作为一个应用程序，我们展示了如何字符串在一个有限的字母表可以编码在分圆扩展的$\mathbb{Q}_p$和讨论$p$ -进DNA编码。该应用程序导致快速$p$ -adic凝聚分层算法类似于最近使用的，例如由A。赫伦尼科夫和其他人。从$p$几何的观点来看，在$p$域$K$中编码树状图$X$意味着在$p$-adic投影线$\mathbb{P}^1$上固定一个$K$ -有理穿刺集$S$.对于$\mathbb{P}^1\setminus S$，以自然的方式将恢复$X$的Bruhat-Tits树内的子树相关联，这是F. Kato于1999年在$\textrm{PGL}_2(K)$的离散亚组分类中。接下来，我们展示了如何$p$ -进模空间$\mathfrak{M}_{0,n}$的$\mathbb{P}^1$与$n$穿刺可以应用于研究的时间序列的树状图和那些对称性所产生的双曲行动$\mathbb{P}^1$。通过这种方式，我们可以将Mumford曲线与某些类别的动力系统相关联，即具有完全退化约简模$p$的$p$ -adic代数曲线。最后，给出了我们在$\mathbb{P}^1$上一般离散作用的研究中的一些结果，以及它们与$p$ -adic Hurwitz空间的关系.
英文摘要：
In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
