Geometric properties of Julia sets of the composition of polynomials of the form z2 + cn
Geometric properties of Julia sets of the composition of polynomials of the form z2 + cn
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z2 cn 形式的多项式组合的 Julia 集的几何性质
DOI：
10.2140/pjm.2001.198.347
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发表时间：
2001
影响因子：
0.6
通讯作者：
R. Brück
中科院分区：
文献类型：
--
作者：
R. Brück
对于复数序列（cn），我们考虑二次多项式fcn（z）：= z 2 + cn和迭代序列（Fn）Fn：= fcn o···o fc1。Fatou集F（cn）定义为所有z ∈ N使得（Fn）在z的某个邻域正规的集合，而F（cn）的补集称为Julia集J（cn）。在序列（cn）有界的条件下，研究了Julia集J（cn）的几何性质、Lebesgue测度和Hausdorff维数.
For a sequence (cn) of complex numbers we consider the quadratic polynomials fcn(z) := z 2 + cn and the sequence (Fn) of iterates Fn := fcn ◦ · · · ◦ fc1 . The Fatou set F(cn) is by definition the set of all z ∈ Ĉ such that (Fn) is normal in some neighbourhood of z, while the complement of F(cn) is called the Julia set J(cn). The aim of this article is to study geometric properties, Lebesgue measure and Hausdorff dimension of the Julia set J(cn) provided that the sequence (cn) is bounded.