Hausdorff dimension of escaping sets of meromorphic functions II

Magnus Aspenberg, Weiwei Cui

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

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[ $4$ ]]>.

Originalspråkengelska
TidskriftErgodic Theory and Dynamical Systems
DOI
StatusAccepted/In press - 2022

Bibliografisk information

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

Ämnesklassifikation (UKÄ)

  • Matematisk analys

Fingeravtryck

Utforska forskningsämnen för ”Hausdorff dimension of escaping sets of meromorphic functions II”. Tillsammans bildar de ett unikt fingeravtryck.

Citera det här