Arboreal Galois groups of rational maps with nonreal Julia sets
Number Theory
2024-12-05 v1 Dynamical Systems
Abstract
We prove a non-abelian arboreal Galois group result for certain maps with non-real Julia set at an archimedean place. We investigate the question of determining which polynomials defined over have real Julia set. Finally we show that for some certain classes of Latt\`es maps associated to the duplication map on an elliptic curve has non-abelian arboreal Galois groups.
Cite
@article{arxiv.2412.03313,
title = {Arboreal Galois groups of rational maps with nonreal Julia sets},
author = {Chifan Leung},
journal= {arXiv preprint arXiv:2412.03313},
year = {2024}
}