迭代和最小结式
Iteration and the Minimal Resultant
摘要：
令$K$是一个代数闭域，它关于非阿基米得绝对值是完备的，并且令$φ\in K(z)$有度$d\geq 2$。我们刻画了映射的最小结式$φ^n$是由一个简单的公式在$d$，$n$，和最小结式$φ$。我们表明，这样的地图正是那些减少以外的不确定性轨迹$I(d)$，也有半稳定的减少，每一个$φ^n$。我们给出了描述这类映射的两种等价方法，一种是测度论的，另一种是度$d$有理映射的模空间$\mathcal{M}_d$.作为应用，我们给出了满足主要定理条件的映射的对角Arakelov-Green函数的极小值的一个显式公式。我们说明了我们的结果与一些明确的计算的情况下，Lattès映射。
英文摘要：
Let $K$ be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let $φ\in K(z)$ have degree $d\geq 2$. We characterize maps for which the minimal resultant of an iterate $φ^n$ is given by a simple formula in terms of $d$, $n$, and the minimal resultant of $φ$. We show that such maps are precisely those with reduction outside of an indeterminacy locus $I(d)$ and which also have semi-stable reduction for every iterate $φ^n$. We give two equivalent ways of describing such maps, one measure theoretic and the other in terms of the moduli space $\mathcal{M}_d$ of degree $d$ rational maps. As an application, we are able to give an explicit formula for the minimal value of the diagonal Arakelov-Green's function of a map satisfying the conditions of the main theorem. We illustrate our results with some explicit calculations in the case of the Lattès maps.
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