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

Abstract

We show that for each $d\in (0,2]$ there exists a meromorphic function $f$ such that the inverse function of $f$ has three singularities and the Julia set of $f$ has Hausdorff dimension $d$.

19 pages

References in corpus (2)

• Hyperbolic dimension and radial Julia sets of transcendental functions
• The order conjecture fails in S

Cited by in corpus (1)

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