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math.DS2026
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…
math.DS2026
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…