Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two
Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two
复制标题
逃逸集具有豪斯多夫二维的快速增长全函数
DOI：
10.1007/s11401-019-0146-4
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Zhuan Ye
中科院分区：
文献类型：
--
作者：
Jie Ding;Jun Wang;Zhuan Ye
研究了一类一般位于Eremenko-Lyubich类外且具有无穷增长级的超越整函数，证明了这些整函数的Julia集与逃逸集的交具有全Hausdorff维，并由此得到了它们的逃逸集的Hausdorff测度是无穷的.
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.