Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two
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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.
KeywordsDynamic systems Entire function Julia set Escaping set Hausdorff dimension
2000 MR Subject Classification37F10 37F35 30D05 30D15
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The authors are grateful to the referees for their suggestions and comments which have improved the clarity of the paper.
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