Normal families: New perspectives

被引：297
作者：
Zalcman, L [1 ]
机构：
[1] Bar Ilan Univ, Dept Math & Comp Sci, IL-52900 Ramat Gan, Israel
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 35卷 / 03期
关键词：
normal families; Picard's theorem; algebraic differential equations; julia set; Bloch's principle;
D O I：
10.1090/S0273-0979-98-00755-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper surveys some surprising applications of a lemma characterizing normal families of meromorphic functions on plane domains. These include short and efficient proofs of generalizations of (i) the Picard Theorems, (ii) Gol'dberg's Theorem (a meromorphic function on C which is the solution of a first-order algebraic differential equation has finite order), and (iii) the Fatou-Julia Theorem (the Julia set of a rational function of degree d greater than or equal to 2 is the closure of the repelling periodic points). We also discuss Bloch's Principle and provide simple solutions to some problems of Hayman connected with this principle.
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收藏
页码：215 / 230
页数：16
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