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Absence of bounded-orbit wandering domains

Nikolai Prochorov, Lasse Rempe, James Waterman

Palomar Registrypalomar/PALOMAR-2026-09-25-000001Oct 1, 2026math.DSscore 0

We formalise the proof of two major recent results on wandering domains of transcendental entire and meromorphic functions: every orbit in a wandering domain accumulates at infinity and at a non-isolated (derived) point of the spherical set of singular values. Both results are obtained as a special case of a more general theorem, for locally defined functions on possibly disconnected complex one-manifolds. Let f be an open holomorphic function from an open subset O of such a manifold X into X. Different components of O may map to different components of X, even when those source components…

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