动力学多项式、项链算子和动力学单位的普遍关系
Dynatomic polynomials, necklace operators, and universal relations for dynamical units
摘要：
给定一般多项式$f(x)$，广义动力学多项式$Φ_{f,c,d}(x)$恰好在那些$α$处为零，使得在$f(x)$的迭代下，$f^c(α)$的周期恰好为$d$。证明了移位动力学多项式$Φ_{f,c,d}(x) - 1$通常具有广义动力学因子，并且这些因子与项链多项式的某些分圆因子相对应. $Φ_{f,c,d}(x) - 1$的这些动力学因子根据在多项式$f(x)$中一致的动力学单元之间的新乘法关系进行解释。
英文摘要：
Given a generic polynomial $f(x)$, the generalized dynatomic polynomial $Φ_{f,c,d}(x)$ vanishes at precisely those $α$ such that $f^c(α)$ has period exactly $d$ under iteration of $f(x)$. We show that the shifted dynatomic polynomials $Φ_{f,c,d}(x) - 1$ often have generalized dynatomic factors, and that these factors are in correspondence with certain cyclotomic factors of necklace polynomials. These dynatomic factors of $Φ_{f,c,d}(x) - 1$ have an interpretation in terms of new multiplicative relations between dynamical units which are uniform in the polynomial $f(x)$.
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