Lebesgue measure of escaping sets of entire functions of completely regular growth

被引：10

作者：

Bergweiler, Walter ^{[1
]}

Chyzhykov, Igor ^{[2
]}

机构：

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

[2] Ivan Franko Natl Univ Lviv, Fac Mech & Math, Univ Ska 1, UA-79000 Lvov, Ukraine

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2016年 / 94卷

关键词：

LINEAR-DIFFERENTIAL EQUATIONS; HAUSDORFF DIMENSION; MEROMORPHIC FUNCTIONS; JULIA SETS; HYPERBOLIC DIMENSION; MAPS;

D O I：

10.1112/jlms/jdw051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give conditions ensuring that the Julia set and the escaping set of an entire function of completely regular growth have positive Lebesgue measure. The essential hypotheses are that the indicator is positive, except perhaps at isolated points, and that most zeros are located in neighborhoods of finitely many rays. We apply the result to solutions of linear differential equations.

引用

页码：639 / 661

页数：23

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