标题： 伯克霍夫不动点轨迹的连通分支 显示英文标题

标题： Connected components of Berkovich fixed point locus

摘要： 设$\mathbb{P}^{1}_{an}$为一个完备、代数闭合、非阿基米德的域上的伯克霍夫射影直线，该域的特征为$0$。 设$\phi$为一个次数为$\geq 2$的有理映射，并且具有潜在良好约化，作用在$\mathbb{P}^{1}_{an}$上。 在本文中，我们给出了$\phi$的不动点轨迹为连通的易于验证的等价条件。 我们还给出了$\phi$的不动点轨迹为有限的等价条件。 此外，我们提供了具有潜在良好约化的有理映射的不动点轨迹的连通分支数的一个紧上界。 显示英文摘要

摘要： Let $\mathbb{P}^{1}_{an}$ be the Berkovich projective line over a complete, algebraically closed, non-Archimedean field of characteristic $0$. Let $\phi$ be a degree $\geq 2$ rational map with potential good reduction, acting on $\mathbb{P}^{1}_{an}$. In this article, we give an easily verifiable equivalent criterion for the fixed point locus of $\phi$ to be connected. We also give an equivalent criterion for the fixed point locus of $\phi$ to be finite. Moreover, we provide a sharp upper bound for the number of connected components of the fixed point locus of a rational map with potential good reduction.