论文标题
后犯有限有限理性地图及其最大扩展商的规范分解
A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients
论文作者
论文摘要
我们根据其朱莉娅集合的拓扑结构提供了在后犯有限的有限理性地图的天然规范分解。该分解的基础是地图，所有FATOU组件都是约旦磁盘，具有隔离闭合（Sierpiński地图），以及那些可以通过具有共同边界点的Fatou组件连接的任何两个FATOU组件（Crocket或Newton likike Map）。我们为分解提供了几种替代特征，以及用于其有效计算的算法。我们还表明，后有限的有限理性地图具有动态自然的商，其中所有钩针编织图都折叠到点，而所有Sierpiński地图变成了小球。商是一种最大的扩展仙人掌。该结构在Böttcher扩展图的更一般设置中起作用，这些图是后批判性有限理性地图的度量模型。
We provide a natural canonical decomposition of postcritically finite rational maps with non-empty Fatou sets based on the topological structure of their Julia sets. The building blocks of this decomposition are maps where all Fatou components are Jordan disks with disjoint closures (Sierpiński maps), as well as those where any two Fatou components can be connected through a countable chain of Fatou components with common boundary points (crochet or Newton-like maps). We provide several alternative characterizations for our decomposition, as well as an algorithm for its effective computation. We also show that postcritically finite rational maps have dynamically natural quotients in which all crochet maps are collapsed to points, while all Sierpiński maps become small spheres; the quotient is a maximal expanding cactoid. The constructions work in the more general setup of Böttcher expanding maps, which are metric models of postcritically finite rational maps.
