论文标题
二次多项式家族的功能图
Functional graphs of families of quadratic polynomials
论文作者
论文摘要
我们研究了由几个二次多项式产生的功能图，同时作用于有限特征的有限场。我们获得了有关此类叶子数量的几个结果。特别是，对于由三个多项式产生的图，我们将叶子的分布与椭圆曲线的Frobenius痕迹的Sato-Tate分布联系起来。我们还提出了广泛的数值结果，我们希望这可以阐明较大的多项式家族的叶子分布。
We study functional graphs generated by several quadratic polynomials, acting simultaneously on a finite field of odd characteristic. We obtain several results about the number of leaves in such graphs. In particular, in the case of graphs generated by three polynomials, we relate the distribution of leaves to the Sato-Tate distribution of Frobenius traces of elliptic curves. We also present extensive numerical results which we hope may shed some light on the distribution of leaves for larger families of polynomials.
