English

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

R2 v1 2026-07-01T03:56:21.062Z