论文标题
仿期平面常规多项式自动形态的几何动力学属性
The Geometric Dynamical Northcott Property For Regular Polynomial Automorphisms of the Affine Plane
论文作者
论文摘要
我们确定了周期点的有限性，即我们称为几何动力学诺斯科特属性，用于仿射平面的常规多项式自动形态，在功能场$ \ mathbf {k} $ a的特征零，从而改善了Ingram的结果。 为此，我们表明，当$ \ mathbf {k} $是光滑的复杂射击曲线的理性函数的字段时，下尺寸的典型高度是适当的分叉电流的质量，并且当它的规范高度为零时，明显的点稳定。然后，我们使用相似性参数建立了几何动力学属性。
We establish the finiteness of periodic points, that we called Geometric Dynamical Northcott Property, for regular polynomials automorphisms of the affine plane over a function field $\mathbf{K}$ of characteristic zero, improving results of Ingram. For that, we show that when $\mathbf{K}$ is the field of rational functions of a smooth complex projective curve, the canonical height of a subvariety is the mass of an appropriate bifurcation current and that a marked point is stable if and only if its canonical height is zero. We then establish the Geometric Dynamical Northcott Property using a similarity argument.
