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