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