Work

Wandering exposed Julia components of rational maps

Year: 2026

Type: preprint

Abstract: We prove that every wandering exposed Julia component of a rational map is a point. Here a Julia component is exposed if it meets the boundary of a Fatou domain. The theorem extends the corresponding result for polynomials to rational maps, without any assumption on critical recurrence. The proof combines an enhanced nest with a covering estimate for multiply connected pullback domains.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31055

Author: Zeng, Jinsong

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7223382278

Cites: 22

Cited by:

Related to: 10