论文标题
理性地图，平滑退化的赫尔曼戒指
Rational maps with smooth degenerate Herman rings
论文作者
论文摘要
我们证明了具有平稳归化的赫尔曼戒指的理性地图的存在。这回答了Eremenko的问题。证明是基于Avila，Buff和Chéritat的平滑Siegel磁盘以及经典的Siegel-Herman-Herman准文献手术的构建。证据中的关键成分是手术的连续性，这取决于Buff和Chéritat二次填充朱莉娅套装区域的损失。 作为副产品，我们证明存在理性地图的存在，这些地图没有一个茂密的朱莉娅（Julia）的积极区域，这些地图没有非理性的漠不关心的周期性点，没有赫尔曼（Herman）戒指，也不可重新分配。
We prove the existence of rational maps having smooth degenerate Herman rings. This answers a question of Eremenko affirmatively. The proof is based on the construction of smooth Siegel disks by Avila, Buff and Chéritat as well as the classical Siegel-to-Herman quasiconformal surgery. A crucial ingredient in the proof is the surgery's continuity, which relies on the control of the loss of the area of quadratic filled-in Julia sets by Buff and Chéritat. As a by-product, we prove the existence of rational maps having a nowhere dense Julia set of positive area for which these maps have no irrationally indifferent periodic points, no Herman rings, and are not renormalizable.
