Periodic points and normal families
Periodic points and normal families
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DOI：
10.1090/s0002-9939-01-05864-6
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发表时间：
2001-02
期刊：
影响因子：
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通讯作者：
D. Bargmann;W. Bergweiler
中科院分区：
文献类型：
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作者：
D. Bargmann;W. Bergweiler
设F是在某一区域上全纯且周期不大于1的周期点的所有函数族。证明了F是拟正规的，并刻画了F中没有收敛子序列的序列。该方法还给出了超越整函数有无穷多个周期点大于1的结果的新证明。
Let F be the family of all functions which are holomorphic in some domain and do not have periodic points of some period greater than one there. It is shown that F is quasinormal, and the sequences in F which do not have convergent subsequences are characterized. The method also yields a new proof of the result that transcendental entire functions have infinitely many periodic points of all periods greater than one.