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Postcritically finite endomorphisms II: Fatou sets
Abstract
Let f be a postcritically finite endomorphism of the complex projective space ℙN of degree at least two. We prove that every Fatou component of f is preperiodic to the basin of a superattracting periodic orbit.
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BibTeX
@misc{sun2026postcritically,
title = {{Postcritically finite endomorphisms II: Fatou sets}},
author = {Ruiran Sun and Shengyuan Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12246},
eprint = {2610.12246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12246},
}
RIS
TY - UNPB
TI - Postcritically finite endomorphisms II: Fatou sets
AU - Ruiran Sun
AU - Shengyuan Zhao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12246
UR - https://arxiv.org/abs/2610.12246
AB - Let f be a postcritically finite endomorphism of the complex projective space ℙ^N of degree at least two. We prove that every Fatou component of f is preperiodic to the basin of a superattracting periodic orbit.
ER -