单临界多项式族中的Nevanlinna理论和value distribution
Nevanlinna theory and value distribution in the unicritical polynomials family
摘要：
在$d>1$次单临界多项式族$f(λ,z)=f_λ(z)=z^d+λ$的参数$λ$的空间$\mathbb{C}$中，建立了分叉电流的定量等分布结果（实际上测量）$f$的$T_f$作为所有参数$λ$的平均分布上的$n\to\infty$，使得$f_λ$在$\mathbb{C}$中具有周期$n$的超吸引周期点，具体的误差估计$C^2$ -测试功能$\mathbb{P}^1$。在证明中，不仅复杂的动力学，而且从Nevanlinna理论的标准参数发挥关键作用。
英文摘要：
In the space $\mathbb{C}$ of the parameters $λ$ of the unicritical polynomials family $f(λ,z)=f_λ(z)=z^d+λ$ of degree $d>1$, we establish a quantitative equidistribution result towards the bifurcation current (indeed measure) $T_f$ of $f$ as $n\to\infty$ on the averaged distributions of all parameters $λ$ such that $f_λ$ has a superattracting periodic point of period $n$ in $\mathbb{C}$, with a concrete error estimate for $C^2$-test functions on $\mathbb{P}^1$. In the proof, not only complex dynamics but also a standard argument from the Nevanlinna theory play key roles.
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