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Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

Authors
  • Ding, Jie1
  • Wang, Jun2
  • Ye, Zhuan1, 3
  • 1 Taiyuan University of Technology, School of Mathematics, Taiyuan, 030024, China , Taiyuan (China)
  • 2 Fudan University, School of Mathematics, Shanghai, 200433, China , Shanghai (China)
  • 3 Univeristy of North Carolina Wilmington, Department of Mathematics and Statistics, Wilmington, NC, 28403, USA , Wilmington (United States)
Type
Published Article
Journal
Chinese Annals of Mathematics, Series B
Publisher
Springer Berlin Heidelberg
Publication Date
Jun 14, 2019
Volume
40
Issue
4
Pages
481–494
Identifiers
DOI: 10.1007/s11401-019-0146-4
Source
Springer Nature
Keywords
License
Yellow

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.

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