415 citations · 1.2k across the 61 of their papers we have counts for
5 papers · 1 filter
Some examples of Baker domains
Walter Bergweiler, Jian-Hua Zheng
We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domain…
Multiply connected wandering domains of entire functions
Walter Bergweiler, Philip J. Rippon, Gwyneth M. Stallard
The dynamical behaviour of a transcendental entire function in any periodic component of the Fatou set is well understood. Here we study the dynamical behaviour of a transcendental…
A property of the derivative of an entire function
Walter Bergweiler, Alexandre Eremenko
We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.
Fatou-Julia theory for non-uniformly quasiregular maps
Walter Bergweiler
Many results of the Fatou-Julia iteration theory of rational functions extend to uniformly quasiregular maps in higher dimensions. We obtain results of this type for certain classe…
On the packing dimension of the Julia set and the escaping set of an entire function
Walter Bergweiler
We show that for large classes of entire functions the Julia set and the escaping set have packing dimension two. For example, this is the case for entire functions which are bound…