AI 中文总结
针对非阿基米德域上Berkovich直线的有理函数作用，引入压缩域概念并证明其含经典不动点，据此给出不动点集连通分支数的精确上界，还利用未发表公式给出多项式情形的另一证明及关键权重显式公式。
AI 中文摘要
我们针对完全非平凡赋值的代数闭非阿基米德域上Berkovich射影直线的有理函数作用，引入“压缩域”的概念，证明这类域必包含一个经典不动点，并利用该事实给出有理函数不动点集连通分支数的精确上界。针对多项式函数，我们给出第二个证明，该证明用到Rivera-Letelier此前未发表的质量公式。最后，我们给出压缩域内关键权重的显式公式，该公式是经典不动点数量与边界点数量的函数。
英文摘要
We introduce the notion of a "compressive domain" for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. We prove that such a domain always contains a classical fixed point, and we leverage this fact to give a sharp upper bound for the number of connected components of the fixed locus of a rational function. We give a second proof for polynomial functions that uses a previously unpublished mass formula of Rivera-Letelier. Finally, we give an explicit formula for the crucial weight inside a compressive domain as a function of the number of classical fixed points and boundary points.
Comments24 pages
