415 citations · 1.2k across the 61 of their papers we have counts for
3 papers · 2 filters
Meromorphic functions with linearly distributed values and Julia sets of rational functions
Walter Bergweiler, Alexandre Eremenko
If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We includ…
The growth rate of an entire function and the Hausdorff dimension of its Julia set
Walter Bergweiler, Bogusława Karpińska, Gwyneth M. Stallard
Let f be a transcendental entire function in the Eremenko-Lyubich class B. We give a lower bound for the Hausdorff dimension of the Julia set of f that depends on the growth of f.…
The escaping set of a quasiregular mapping
Walter Bergweiler, Alastair Fletcher, Jim Langley +1
We show that if the maximum modulus of a quasiregular mapping f grows sufficiently rapidly then there exists a non-empty escaping set I(f) consisting of points whose forward orbits…