A class of Latt\`es maps with cellular structures
Dynamical Systems
2025-12-02 v1 Complex Variables
Abstract
We show that a class of quasiregular Latt\`es maps, called orthotopic Latt\`es maps, are cellular Markov maps. This provides examples of expanding Thurston-type maps that are also uniformly quasiregular, and whose visual metrics are quasisymmetrically equivalent to the Riemannian distance.
Keywords
Cite
@article{arxiv.2512.00372,
title = {A class of Latt\`es maps with cellular structures},
author = {Zhiqiang Li and Hanyun Zheng},
journal= {arXiv preprint arXiv:2512.00372},
year = {2025}
}
Comments
16 pages, 4 figures