多项式的Mandelbrot集和伽罗瓦群的内部地址
Internal addresses in the Mandelbrot set and Galois groups of polynomials
摘要：
我们描述了一个有趣的符号动力学之间的相互作用，结构的Mandelbrot集，置换的周期点实现的解析延拓，和伽罗瓦群的某些多项式。内部地址是描述曼德布罗特集的组合结构的一种方便而有效的方法，并且以人类可读的形式为无处不在的揉捏序列赋予几何意义（第3节和第4节）。一个单扩张，\emph{angled internal addresses}，区分组合类的曼德尔布罗特集，特别是区分双曲成分在一个简洁和动态有意义的方式。Mandelbrot集的这种组合描述使我们有可能导出Mandelbrot集中某些揉序列和内部地址的存在性定理（第6节），并给出相关参数的显式描述。这些又有助于建立关于周期点置换的一些代数结果和确定某些多项式的伽罗瓦群（第7节）。通过内部地址，本手稿涉及数学的各个领域，包括符号动力学和置换、曼德尔布罗特集的组合学和伽罗瓦群。
英文摘要：
We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a convenient and efficient way of describing the combinatorial structure of the Mandelbrot set, and of giving geometric meaning to the ubiquitous kneading sequences in human-readable form (Sections 3 and 4). A simple extension, \emph{angled internal addresses}, distinguishes combinatorial classes of the Mandelbrot set and in particular distinguishes hyperbolic components in a concise and dynamically meaningful way. This combinatorial description of the Mandelbrot set makes it possible to derive existence theorems for certain kneading sequences and internal addresses in the Mandelbrot set (Section~6) and to give an explicit description of the associated parameters. These in turn help to establish some algebraic results about permutations of periodic points and to determine Galois groups of certain polynomials (Section~7). Through internal addresses, various areas of mathematics are thus related in this manuscript, including symbolic dynamics and permutations, combinatorics of the Mandelbrot set, and Galois groups.
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。
