Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

【Author】

Jie DING;Jun WANG;Zhuan YE;School of Mathematics, Taiyuan University of Technology;School of Mathematics, Fudan University;Department of Mathematics and Statistics, Univeristy of North Carolina Wilmington;

【Institution】

School of Mathematics, Taiyuan University of Technology;School of Mathematics, Fudan University;Department of Mathematics and Statistics, Univeristy of North Carolina Wilmington;

【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;;Hausdorff dimension

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