2019/08/20 by William Floyd, Floyd, William, Walter Parry +3
Computer Science · Mathematics · #37F19 #52C20 (Primary) #57M12 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37F19 #msc:52C20 #msc:57M12 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1908.07571
24 pages, 7 figures
arxiv created 2019/08/20 · openalex publication_date 2019/08/20 · arxiv updated 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivision map of a finite subdivision rule. We determine which Thurston maps doubly covered by a torus endomorphism have iterates that are isotopic to subdivision maps of finite subdivision rules. We give conditions under which no iterate of a given Thurston map is isotopic to the subdivision map of a finite subdivision rule.