Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

Citation:

Jie DING,Jun WANG,Zhuan YE.Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two[J].Chinese Annals of Mathematics B,2019,40(4):481~494
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Authors:

Jie DING; Jun WANG;Zhuan YE

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11601362, 11771090, 11571049) and the Natural Science Foundation of Shanghai (No.17ZR1402900).
Abstract: 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.

Keywords:

Dynamic systems, Entire function, Julia set, Escaping set, Hausdorffdimension

Classification:

37F10, 37F35, 30D05, 30D15
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