We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of their Galois groups as subgroups of automorphism groups of regular trees, in terms of iterated wreath products. This allows us to study the behavior of the monodromy groups under specialization of the maps, and to derive applications to dynamical sequences.

中文翻译：

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动力学 Belyi 映射和树栖伽罗瓦群

我们考虑一大类所谓的动态 Belyi 映射，并研究这些映射的迭代伽罗瓦群。从映射的组合不变量，我们构造了一个有用的表示，将它们的伽罗瓦群作为常规树的自同构群的子群，就迭代花环积而言。这使我们能够在地图的专业化下研究单向群的行为，并推导出对动力学序列的应用。