A class of Lattès maps with cellular structures

2025/11/29 by Zhiqiang Li, Li, Zhiqiang, Zheng, Hanyun
Computer Science · Mathematics · #30L10 #37F15 #37F20 #37F31 #Cellular Automata and Applications #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 37F10 #Secondary: 30C65 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2512.00372

openalex publication_date 2025/11/29 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We show that a class of quasiregular Lattès maps, called orthotopic Lattès 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.

Citations

• Rigidity and quasisymmetric uniformization of Thurston-type maps
• Notes on quasiregular maps between Riemannian manifolds

Related

• Perturbations of flexible Lattès maps
• Length-expanding Lipschitz maps on totally regular continua
• Hyperbolic and Parabolic Unimodular Random Maps
• Lattes maps on P²
• Cellular Automata vs. Quasisturmian Shifts