Rempe, Lasse and Stallard, Gwyneth M.
Hausdorff dimensions of escaping sets of transcendental entire functions.
Proceedings of the American Mathematical Society, 138(5) pp. 1657–1665.
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Suppose that f and g are transcendental entire functions, each with a bounded set of singular values, and that f and g are affinely equivalent. We show that the escaping sets of f and g have the same Hausdorff dimension.
Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equal to one.
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