PreprintCC BY 4.0arXiv
Wandering exposed Julia components of rational maps
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.
Related
- Uniformization of Julia sets of geometrically finite rational maps
- Wandering continua, renormalization, and Lebesgue measure on Julia sets
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- On the Julia sets of the non-autonomous iteration of exponential maps
- Higher arithmetic degrees of dominant rational self-maps
BibTeX
@misc{zeng2026wandering,
title = {{Wandering exposed Julia components of rational maps}},
author = {Jinsong Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31055},
eprint = {2610.31055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31055},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Wandering exposed Julia components of rational maps
AU - Jinsong Zeng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31055
UR - https://arxiv.org/abs/2610.31055
AB - 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.
ER -