# Hausdorff dimension of escaping sets of meromorphic functions II

Magnus Aspenberg, Weiwei Cui

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## Sammanfattning

A function which is transcendental and meromorphic in the plane has at least two singular values. On the 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 <![CDATA[ \$2\$ ]]> or <![CDATA[ \$1/2\$ ]]>. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in <![CDATA[ \$[0,2]\$ ]]> (cf. [M. Aspenberg and W. Cui. Hausdorff dimension of escaping sets of meromorphic functions. Trans. Amer. Math. Soc. 374(9) (2021), 6145-6178]). 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 <![CDATA[ \$4\$ ]]>.

Originalspråk engelska Ergodic Theory and Dynamical Systems https://doi.org/10.1017/etds.2022.5 Accepted/In press - 2022