415 citations · 1.2k across the 61 of their papers we have counts for
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math.CV2007★ 7 cited
Newton's method and Baker domains
Walter Bergweiler
We show that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic functions without Baker doma…
math.CV2007★ 27 cited
An entire function with simply and multiply connected wandering domains
Walter Bergweiler
We modify a construction of Kisaka and Shishikura to show that there exists an entire function which has both a simply connected and a multiply connected wandering domain. Moreover…
math.CV2007★ 50 cited
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…