4 citations · 8 across the 5 of their papers we have counts for
8 papers
Absence of bounded-orbit wandering domains
Nikolai Prochorov, Lasse Rempe, James Waterman
We prove that transcendental entire functions do not have bounded-orbit wandering domains. This answers a long-standing open question. In fact, we prove a more general theorem, est…
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…
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…
Wiman-Valiron discs and the dimension of Julia sets
James Waterman
We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on t…
Identifying logarithmic tracts
James Waterman
We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an applicat…
Slow escape in tracts
James Waterman
Let be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove…
On the infinitesimal space of uqr mappings
Alastair Fletcher, Doug Macclure, James Waterman +1
Generalized derivatives and infinitesimal spaces generalize the idea of derivatives to mappings which need not be differentiable. It is particularly powerful in the context of quas…