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Rempe, Lasse and Stallard, Gwyneth M.
(2010).
URL: http://www.ams.org/journals/proc/2010-138-05/S0002...
Abstract
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.