526 citations
- Gemini North ObservatoryUS3 papers
- Ruhr University BochumDE3 papers
- Universidade Federal do Rio Grande do SulBR3 papers
- Universität GreifswaldDE3 papers
- Leipzig UniversityDE2 papers
- Max Planck Institute for AstrophysicsDE2 papers
- Max Planck Institute for Extraterrestrial PhysicsDE2 papers
- Örebro UniversitySE2 papers
- Purdue University West LafayetteUS2 papers
- Russian Academy of SciencesRU2 papers
- The University of Texas at AustinUS2 papers
- Universidad Nacional de La PlataAR2 papers
4 papers · 1 filter
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 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…
Dynamics of meromorphic functions with direct or logarithmic singularities
Walter Bergweiler, Philip J. Rippon, Gwyneth M. Stallard
We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Ju…
Real entire functions with real zeros and a conjecture of Wiman
Walter Bergweiler, A. Eremenko, J. K. Langley
If f is a real entire function and ff" has only real zeros then f belongs to the Laguerre-Polya class, the closure of the set of real polynomials with real zeros. This result compl…