We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those that vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.

中文翻译：

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乘数的度数差距和动力学 André-Oort 猜想

我们展示了 Favre 和 Gauthier 的最新工作以及作者对结果的修改，表明具有无限多个后临界有限特化的多项式族不能有任何具有非常低阶乘数的周期循环，除了那些消失，概括了 Baker 和 DeMarco 以及 Favre 和 Gauthier 的结果。