415 citations · 1.2k across the 61 of their papers we have counts for
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On the Hausdorff dimension of the Julia set of a regularly growing entire function
Walter Bergweiler, Bogusława Karpińska
We show that if the growth of a transcendental entire function f is sufficiently regular, then the Julia set and the escaping set of f have Hausdorff dimension 2.
Entire functions with Julia sets of positive measure
Magnus Aspenberg, Walter Bergweiler
Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for w…
Karpińska's paradox in dimension three
Walter Bergweiler
For 0 < c < 1/e the Julia set of f(z) = c exp(z) is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of…
On the Hausdorff dimension of the escaping set of certain meromorphic functions
Walter Bergweiler, Janina Kotus
The escaping set I(f) of a transcendental meromorphic function f consists of all points which tend to infinity under iteration. The Eremenko-Lyubich class B consists of all transce…