English

Non-recurrent rational maps with disconnected Julia set

Dynamical Systems 2025-09-09 v1

Abstract

We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent. Moreover, we show that the Julia set contains only finitely many periodic complex-type components if each wandering Julia component containing critical values is non-recurrent.

Keywords

Cite

@article{arxiv.2509.06645,
  title  = {Non-recurrent rational maps with disconnected Julia set},
  author = {Yan Gao and Lele Xu and Luxian Yang},
  journal= {arXiv preprint arXiv:2509.06645},
  year   = {2025}
}

Comments

13 pages, 4 figures

R2 v1 2026-07-01T05:26:21.966Z