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| Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two |
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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 |
| Page view： 1329
Net amount： 1246 |
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). |
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| 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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