The Medusa algorithm for polynomial matings
The Medusa algorithm for polynomial matings
复制标题
用于多项式交配的 Medusa 算法
DOI：
10.1090/s1088-4173-2012-00245-7
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Christian Henriksen
中科院分区：
文献类型：
--
作者：
Suzanne Boyd;Christian Henriksen
Medusa算法以两个后临界有限二次多项式作为输入，并输出作为两个多项式的配对的二次有理映射（如果存在）。具体来说，输出是有理映射参数的一系列近似，以及其Julia集的图像。这些近似是否收敛的回答使用瑟斯顿的拓扑表征的理性地图。
该算法由John Hamal Hubbard设计，并于1998年由Christian Henriksen和REU学生大卫法里斯和Kuon Ju Liu实现。本文描述了该算法及其实现，讨论了程序的输出（包括许多图片）和相关问题。具体来说，我们包括图像和讨论一些共享的交配，拉茨的例子，和调整序列的交配。
The Medusa algorithm takes as input two postcritically finite quadratic polynomials and outputs the quadratic rational map which is the mating of the two polynomials (if it exists). Specifically, the output is a sequence of approximations for the parameters of the rational map, as well as an image of its Julia set. Whether these approximations converge is answered using Thurston's topological characterization of rational maps.
This algorithm was designed by John Hamal Hubbard, and implemented in 1998 by Christian Henriksen and REU students David Farris, and Kuon Ju Liu. In this paper we describe the algorithm and its implementation, discuss some output from the program (including many pictures) and related questions. Specifically, we include images and a discussion for some shared matings, Lattes examples, and tuning sequences of matings.