Year: 2026
Type: preprint
Abstract: We give a new elementary proof of Sullivan's no-wandering-domain theorem for rational maps of degree at least two using hyperbolic area. We then develop this method further to prove that a transcendental entire function has no wandering Fatou components if its set of singular values is compact and all accumulation points of that set lie in the Fatou set. Neither proof uses quasiconformal techniques.
Source: arXiv (Cornell University)
Author: Ye, Zihao
Institution: East China Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214019188