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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{prochorov2026absence,
  title = {{Absence of bounded-orbit wandering domains}},
  author = {Nikolai Prochorov and Lasse Rempe and James Waterman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28279},
  eprint = {2609.28279},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28279},
}
RIS
TY  - UNPB
TI  - Absence of bounded-orbit wandering domains
AU  - Nikolai Prochorov
AU  - Lasse Rempe
AU  - James Waterman
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28279
UR  - https://arxiv.org/abs/2609.28279
AB  - 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.
ER  -