Most Fatou and Julia components are small for polynomials
Dynamical Systems
2025-07-14 v1
Abstract
We prove that Julia components of polynomials are generally small in diameter. For polynomials without irrationally neutral cycles, Fatou components are also typically small, even when the Julia set is not locally connected.
Keywords
Cite
@article{arxiv.2507.08471,
title = {Most Fatou and Julia components are small for polynomials},
author = {Jinsong Zeng},
journal= {arXiv preprint arXiv:2507.08471},
year = {2025}
}
Comments
17 pages, 1 figures