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arXiv · 2609.28279

Absence of bounded-orbit wandering domains

Nikolai Prochorov·Lasse Rempe·James Waterman
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Abstract

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, establishing the absence of certain wandering domains even for locally defined analytic functions. The proof is based on a recent remarkable argument of Ye, who obtained an elementary proof of Sullivan's classical theorem that rational maps do not have wandering domains.

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Nikolai Prochorov, Lasse Rempe, James Waterman. 2026-09-23. Absence of bounded-orbit wandering domains. https://arxiv.org/abs/2609.28279

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