The Spider Algorithm
The Spider Algorithm
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蜘蛛算法
DOI：
10.1090/psapm/049/1315537
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发表时间：
2006
影响因子：
0.7
通讯作者：
D. Schleicher
中科院分区：
文献类型：
--
作者：
J. Hubbard;D. Schleicher
复杂分析动力学之所以成为一门如此成功的学科，原因之一是保角映射、动力学和组合学之间已经浮出水面的深层次联系。蜘蛛算法的目标是构造具有指定组合的多项式。当你试图理解曼德尔布洛特集时，这一点就会显现出来。在这个讨论中，我们将写成我们的二次多项式qc(Z)=z+c。每个这样的多项式都有一个填充Julia集Kc，它是由Qc迭代下有界轨道的点组成的。Fatou的一个结果断言，如果临界点0∈Kc，则Kc是连通的，如果0/∈Kc，则Kc是康托集。根据定义，Mandelbrot集M是与Kc相连的c的集合。设D表示开单位圆盘，ΦM：C−M→C−D是从∞到∞且在无穷远处与恒等式相切的保形映射。这种映射的存在并不明显；它被证明与
One of the reasons complex analytic dynamics has been such a successful subject is the deep relation that has surfaced between conformal mapping, dynamics and combinatorics. The object of the spider algorithm is to construct polynomials with assigned combinatorics. This shows up when you try to understand the Mandelbrot set. For this discussion we will write our quadratic polynomials Qc(z) = z + c. Every such polynomial has a filled in Julia set Kc, formed of the points with bounded orbits under iteration of Qc. A result of Fatou asserts that if the critical point 0 ∈ Kc, then Kc is connected, and if 0 / ∈ Kc, then Kc is a Cantor set. By definition, the Mandelbrot set M is the set of c for which Kc is connected. Let D denote the open unit disc, and let ΦM : C−M → C−D be the conformal mapping which maps ∞ to ∞ and is tangent to the identity at infinity. The existence of this mapping is not obvious; it is proved to exist at the same time as the