论文标题
无数地图家庭中的啤酒切片
Bers Slices in Families of Univalent Maps
论文作者
论文摘要
我们构建理想多边形反射组的啤酒切片的嵌入到古典函数$σ$的古典家族中。这种嵌入使得反射组与反塑形多项式$ z \ mapsto \ edline {z}^d $的保形交配是由$σ$中相应的映射产生的schwarz反射图。我们将这种嵌入$σ$的图像描述为一个单价合理地图的家族。此外，我们表明，在bers片关闭中，每个克莱恩反射组的极限集自然是抗孤晶多项式的朱莉娅集合。
We construct embeddings of Bers slices of ideal polygon reflection groups into the classical family of univalent functions $Σ$. This embedding is such that the conformal mating of the reflection group with the anti-holomorphic polynomial $z\mapsto\overline{z}^d$ is the Schwarz reflection map arising from the corresponding map in $Σ$. We characterize the image of this embedding in $Σ$ as a family of univalent rational maps. Moreover, we show that the limit set of every Kleinian reflection group in the closure of the Bers slice is naturally homeomorphic to the Julia set of an anti-holomorphic polynomial.
