Hausdorff dimensions of escaping sets of transcendental entire functions

Rempe, Lasse and Stallard, Gwyneth M. (2010). Hausdorff dimensions of escaping sets of transcendental entire functions. Proceedings of the American Mathematical Society, 138(5) pp. 1657–1665.

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.

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