论文标题
关于Denjoy-Wolff点的收敛
On the convergence of Denjoy-Wolff points
论文作者
论文摘要
如果$φ$是单位磁盘$ \ mathbb {d} $的分析函数，而$φ$并不是保形的自动形态，那么我们用$λ_φ$表示denjoy-wolff点，即iTerates $φ（φ（φ（xotsvotsvotnvomv））的极限。 Heins的结果表明，给定序列$（φ_{n}）_ {n \ in \ Mathbb {n}} $的这种分析函数，这些函数将其汇聚到$φ$，它遵循$ \ lim_ {n \ to \ lim_ {n \ to \ infty}}λ_ /λ_{φ_{φ_{φ这使我们能够改善自由卷积研究中产生的从属函数的串联扩展的结果。我们还提供了Heins结果的替代证明。
If $φ$ is an analytic function from the unit disk $\mathbb{D}$ to itself, and $φ$ is not a conformal automorphism, we denote by $λ_φ$ its Denjoy-Wolff point, that is, the limit of the iterates $φ(φ(\cdotsφ(0)\cdots))$. A result of Heins shows that, given a sequence $(φ_{n})_{n\in\mathbb{N}}$ of such analytic functions that convergence pointwise to $φ$, it follows that $\lim_{n\to\infty}λ_{φ_{n}}=λ_φ$. This allows us to improve results about the contnuous extensions of the subordination functions that arise in the study of free convolutions. We also offer an alternate proof of the result of Heins.
