分支迭代伽罗华群与正固定点比例及正豪斯多夫维度
Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension
AI总结：
本文研究了后临界无限unicritical多项式的算术 profinite 迭代 monodromy 群，证明其具有正豪斯多夫维度和正固定点比例，扩展了正分支群的研究范围。
摘要：
本文证明了后临界无限unicritical多项式的算术 profinite 迭代 monodromy 群是正分支（因此具有正豪斯多夫维度），且当次数为奇数时具有正固定点比例。这些例子属于本文中构造的一类更大的正分支群家族，其固定点比例可以显式计算并在许多情况下为正。这给出了首个不在二进制根树中的例子，其中传递层次的群具有正豪斯多夫维度和正固定点比例，回答了 Jones（2008）的否定性问题。
英文摘要：
In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff dimension), and has positive fixed-point proportion when the degree is odd. The examples are instances of a bigger family of regular branch groups constructed in this article, whose fixed-point proportion can be computed explicitly and is positive in many cases. This gives the first examples outside the binary rooted tree where a level-transitive group has positive Hausdorff dimension and positive fixed-point proportion, answering in the negative a question of Jones (2008).
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