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arXiv · 2209.06270

The Hausdorff dimension of escaping sets of meromorphic functions in the Speiser class

Walter Bergweiler·Weiwei Cui
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Abstract

Bergweiler and Kotus gave sharp upper bounds for the Hausdorff dimension of the escaping set of a meromorphic function in the Eremenko-Lyubich class, in terms of the order of the function and the maximal multiplicity of the poles. We show that these bounds are also sharp in the Speiser class. We apply this method also to construct meromorphic functions in the Speiser class with preassigned dimensions of the Julia set and the escaping set.

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Walter Bergweiler, Weiwei Cui. 2022-09-13. The Hausdorff dimension of escaping sets of meromorphic functions in the Speiser class. https://doi.org/10.1093/imrn%2Frnad126

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