论文标题
与模块化组的二次图的安装
Equidistribution for matings of quadratic maps with the Modular group
论文作者
论文摘要
我们研究了全体形态通讯家族的渐近行为$ \ lbrace \ mathcal {f} _a \ rbrace_ {a \ in \ Mathcal {k}} $，由$ \ left（\ frac {az+1} {z+1} \ right）^2+\左（\ frac {az+1} {z+1} \ right）\ left（\ frac {aw-1} {aw-1} {w-1} {w-1} {w-1} {w-1} {w-1} {w wef）由Bullet和Lomonaco证明，$ \ Mathcal {f} _a $是模块化组$ \ pereratatorName {psl} _2（\ Mathbb {z}）$与二次理性映射之间的交配。我们在\ Mathcal {k} $中显示的每一个$ a \，迭代的图像和预映率在$ \ Mathcal {f} _a _a _a $均等点的_a $，尽管$ \ nathcal {f} _a $是弱模型的事实，即$ \ nathcal {f} _a $是dinh，kaaufmann and kaufmann and iSwue nes n is wu u eus，use nes use nes ute nes ute nes ute nes ute nes ute。此外，我们还证明了定期分配点。
We study the asymptotic behavior of the family of holomorphic correspondences $\lbrace\mathcal{F}_a\rbrace_{a\in\mathcal{K}}$, given by $$\left(\frac{az+1}{z+1}\right)^2+\left(\frac{az+1}{z+1}\right)\left(\frac{aw-1}{w-1}\right)+\left(\frac{aw-1}{w-1}\right)^2=3.$$ It was proven by Bullet and Lomonaco that $\mathcal{F}_a$ is a mating between the modular group $\operatorname{PSL}_2(\mathbb{Z})$ and a quadratic rational map. We show for every $a\in\mathcal{K}$, the iterated images and preimages under $\mathcal{F}_a$ of nonexceptional points equidistribute, in spite of the fact that $\mathcal{F}_a$ is weakly-modular in the sense of Dinh, Kaufmann and Wu but it is not modular. Furthermore, we prove that periodic points equidistribute as well.
