The Polynomials Associated with a Julia Set
The Polynomials Associated with a Julia Set
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与 Julia 集关联的多项式
DOI：
10.1112/blms/27.3.239
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发表时间：
1995
影响因子：
0.9
通讯作者：
W. Schmidt
中科院分区：
文献类型：
--
作者：
N. Steinmetz;W. Schmidt
我们证明了，除了两个例外，具有Julia集J的多项式集具有形式{σ pn：n ∈ N，σ ∈ N}，其中p是这些多项式之一，N是J的对称群.当J是圆或直线段时例外。几篇论文[1，2，3，5]已经出现了处理多项式之间的关系具有相同的朱莉娅集J（符号读者是指[8]）。这个关系非常简单，并不令人惊讶：定理对于任何Julia集（多项式）J，它不是圆或直线段，存在多项式p，使得任何具有Julia集J的多项式都可以写成形式σ pn，其中σ是J到自身的旋转映射，n是正整数。
We prove that, with two exceptions, the set of polynomials with Julia set J has the form {σ pn : n ∈ N , σ ∈ Σ} , where p is one of these polynomials and Σ is the symmetry group of J . The exceptions occur when J is a circle or a straight line segment. Several papers [1, 2, 3, 5] have appeared dealing with the relation between polynomials having the same Julia set J (for notation the reader is referred to [8]). This relation is very simple and by no means surprising: Theorem To any Julia set (of a polynomial) J , which is not a circle or a straight line segment, there exists a polynomial p such that any polynomial with Julia set J can be written in the form σ pn , where σ is a rotation mapping J onto itself, and n is a positive integer.