4 citations · 10 across the 4 of their papers we have counts for
4 papers
A counterexample to Eremenko's conjecture
David Martí-Pete, Lasse Rempe, James Waterman
The escaping set of a transcendental entire function consists of those points that tend to infinity under iteration. Eremenko asked whether every connected component of this set is…
On the dimension of the boundaries of attracting basins of entire maps
Krzysztof Barański, Bogusława Karpińska, David Martí-Pete +2
Let be a transcendental entire map from the Eremenko-Lyubich class , and let be an attracting periodic point of period . We…
Bounded Fatou and Julia components of meromorphic functions
David Martí-Pete, Lasse Rempe, James Waterman
We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fato…
Eremenko's conjecture, wandering Lakes of Wada, and maverick points
David Martí-Pete, Lasse Rempe, James Waterman
We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open prob…