On the Non-existence of Unbounded Domains of Normality of Meromorphic Functions
On the Non-existence of Unbounded Domains of Normality of Meromorphic Functions
复制标题
论亚纯函数无界正规域的不存在性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Zheng Jianhua
中科院分区：
文献类型：
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作者：
Zheng Jianhua
假设f−2∞至少包含三个不同的点，且所有的f n z都在Nf上解析。众所周知，Nf是开的，并且在f下具有完全不变性，即z∈Nf当且仅当f z∈Nf。设U是Nf的分支，则f n U⊆Un，其中Un是Nf的分支。如果对最小整数p>；0 f p U⊆U，则称U为周期p的周期分量。特别地，如果p=1，则称U为不变量。如果对于某个整数n，≥1un是周期的，而U不是周期的，那么U称为准周期的。如果U是周期p的周期分量，且存在∈∂U∪∞使得f z→a在U中为n→∞，且f z不定义在z=a处，则称U为Baker域。此外，设U0 U1向上−1是贝克域的周期循环，
provided that f−2 ∞ contains at least three distinct points, and all of the f n z are analytic on N f . It is well known that N f is open and has the property of complete invariance under f , that is, z ∈ N f if and only if f z ∈ N f . Let U be a component of N f ; then f n U ⊆ Un, where Un is a component of N f . If, for a smallest integer p > 0 f p U ⊆ U , then U is said to be a periodic component of period p. In particular, if p = 1, then U is called invariant. If, for some integer n ≥ 1 Un is a periodic, while U is not periodic, then U is called preperiodic. If U is a periodic component of period p and there exists a ∈ ∂U ∪ ∞ such that f z → a in U as n → ∞, and f z is not defined at z = a, then U is called a Baker domain. Furthermore, let U0 U1 Up−1 be a periodic cycle of Baker domains,