Functions of genus zero for which the fast escaping set has Hausdorff dimension two

Sixsmith, D.

doi:10.1090/S0002-9939-2015-12487-2

Functions of genus zero for which the fast escaping set has Hausdorff dimension two
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Proc. Amer. Math. Soc. 143 (2015), 2597-2612 Request permission

Abstract:

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.

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