论文标题
MISIUREWICZ多项式和动力单位，第二部分
Misiurewicz polynomials and dynamical units, Part II
论文作者
论文摘要
修复整数$ d \ geq 2 $。 $ c_0 \ in \ bar {\ mathbb {q}} $的参数，该$ c_0 \ in \ mathbb {q}} $ commitical polightionalial $ f_ {d，c}（z）= z^d+c \ in \ in \ mathbb {c} [z c} $具有有限的后临界轨道，也众所周知，这也称为MisiureWicz参数，有效地具有重要的作用。 Buff，Epstein和Koch的最新工作证明了使用其算术特性的长期动力学猜想的第一个已知案例，否则知之甚少。继续在同伴论文中进行工作，我们解决了误导性参数的进一步算术特性，尤其是通过评估在不同的Misiurewicz参数下定义一个这样的参数的多项式来获得的代数整数的性质。在最具挑战性的此类组合中，我们描述了此类代数整数与相关周期点的乘数之间的联系。作为我们的考虑的一部分，我们还引入了一种新的多项式类别，我们称为$ p $ - 特别是具有独立数字理论利益。
Fix an integer $d\geq 2$. The parameters $c_0\in \bar{\mathbb{Q}}$ for which the unicritical polynomial $f_{d,c}(z)=z^d+c\in \mathbb{C}[z]$ has finite postcritical orbit, also known as Misiurewicz parameters, play a significant role in complex dynamics. Recent work of Buff, Epstein, and Koch proved the first known cases of a long-standing dynamical conjecture of Milnor using their arithmetic properties, about which relatively little is otherwise known. Continuing our work in a companion paper, we address further arithmetic properties of Misiurewicz parameters, especially the nature of the algebraic integers obtained by evaluating the polynomial defining one such parameter at a different Misiurewicz parameter. In the most challenging such combinations, we describe a connection between such algebraic integers and the multipliers of associated periodic points. As part of our considerations, we also introduce a new class of polynomials we call $p$-special, which may be of independent number theoretic interest.
