Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

作     者：Jie DING Jun WANG Zhuan YE 

作者机构：School of MathematicsTaiyuan University of TechnologyTaiyuan 030024China School of MathematicsFudan UniversityShanghai 200433China Department of Mathematics and StatisticsUniveristy of North Carolina WilmingtonWilmingtonNC 28403USA 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2019年第40卷第4期

页      面：481-494页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11601362,11771090,11571049) the Natural Science Foundation of Shanghai(No.17ZR1402900) 

主　　题：Dynamic systems Entire function Julia set Escaping set Hausdorff dimension 

摘      要：The authors study a family of transcendental entire functions which lie outside the Eremenko-Lyubich class in general and are of infinity growth order. Most importantly,the authors show that the intersection of Julia set and escaping set of these entire functions has full Hausdorff dimension. As a by-product of the result, the authors also obtain the Hausdorff measure of their escaping set is infinity.