论文标题
在具有有限连接的FATOU集的双曲合理图上
On hyperbolic rational maps with finitely connected Fatou sets
论文作者
论文摘要
在本文中，我们研究了具有有限连接的FATOU集合的双曲线理性图。我们为此类地图构建了有限的双曲线树映射方案的模型，在连接的朱莉娅集合的情况下概括了后有限的有限理性地图。我们表明，当我们准确地扩展动力学时，它们是理性地图的一般限制。相反，我们使用准文献手术显示出任何有限的双曲树映射方案，这是这样的限制。 由于模型的灵活性，我们构建了丰富的示例，并使用它们来构建一系列具有无限许多非共同恢复限制的固定程度的理性图。
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct models of post-critically finite hyperbolic tree mapping schemes for such maps, generalizing post-critically finite rational maps in the case of connected Julia set. We show they are general limits of rational maps as we quasiconformally stretch the dynamics. Conversely, we use quasiconformal surgery to show any post-critically finite hyperbolic tree mapping scheme arises as such a limit. We construct abundant examples thanks to the flexibilities of the models, and use them to construct a sequence of rational maps of a fixed degree with infinitely many non-monomial rescaling limits.
