Periodic points and normal families

被引：15

作者：

Bargmann, D ^{[1
]}

Bergweiler, W ^{[1
]}

机构：

[1] Univ Kiel, Math Seminar, D-24098 Kiel, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 10期

关键词：

D O I：

10.1090/S0002-9939-01-05864-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2881 / 2888

页数：8

共 19 条

[1] On the theory of superimposed surfaces
Ahlfors, L
[J]. ACTA MATHEMATICA, 1935, 65 (01) : 157 - 194
[2] AHLFORS LV, 1982, COLLECT PAPERS, V1, P214
[3] [Anonymous], 1991, COMPLEX VARIABLES TH
[4] [Anonymous], 1964, J LONDON MATH SOC
[5] A new proof of the Ahlfors five islands theorem
Bergweiler, W
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1998, 76 (1): : 337 - 347
[6] BERGWEILER W, 1991, THESIS RHEINISCH WES
[7] CARLESON L, 1993, COMPELX DYNAMICS
[8] Chuang C. T., 1993, NORMAL FAMILIES MERO
[9] DOUADY A, 1985, ANN SCI ECOLE NORM S, V18, P287
[10] Repulsive fixpoints of analytic functions with applications to complex dynamics
Essén, M
Wu, SJ
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 62 : 139 - 148

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