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arXiv · 2011.08267

Hausdorff dimension of escaping sets of meromorphic functions II

Magnus Aspenberg·Weiwei Cui
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Abstract

A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either $2$ or $1/2$. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in $[0,2]$ (cf. \cite{ac1}). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than $4$.

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Magnus Aspenberg, Weiwei Cui. 2020-11-16. Hausdorff dimension of escaping sets of meromorphic functions II. https://arxiv.org/abs/2011.08267

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