Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

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

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