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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 481–494 | Cite as

Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

  • Jie Ding
  • Jun Wang
  • Zhuan YeEmail author
Article
  • 8 Downloads

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 Hausdor. dimension. As a by-product of the result, the authors also obtain the Hausdor. measure of their escaping set is infinity.

Keywords

Dynamic systems Entire function Julia set Escaping set Hausdorff dimension 

2000 MR Subject Classification

37F10 37F35 30D05 30D15 

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Notes

Acknowledgement

The authors are grateful to the referees for their suggestions and comments which have improved the clarity of the paper.

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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.School of MathematicsTaiyuan University of TechnologyTaiyuanChina
  2. 2.School of MathematicsFudan UniversityShanghaiChina
  3. 3.Department of Mathematics and StatisticsUniveristy of North Carolina WilmingtonWilmingtonUSA

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