2025/03/13 by Liang-Chung Hsia, Hsia, Liang-Chung, Chenxi Wu +2 · 1 citation
Mathematics · #11S82 #37B40 #37C35 #37E25 #37P05 #37P10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2503.10018
openalex publication_date 2025/03/13 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
Let K be a complete non-archimedean field of characteristic 0 equipped with a discrete valuation. We establish the rationality of the Artin-Mazur zeta function on the Julia set for any subhyperbolic rational map defined over K with a compact Julia set. Furthermore, we conclude that the topological entropy on the Julia set of such a map is given by the logarithm of a weak Perron number. Conversely, we construct a (sub)hyperbolic rational map defined over K with compact Julia set whose topological entropy on the Julia set equals the logarithm of a given weak Perron number. This extends Thurston's work on the entropy for postcritically finite interval self-maps %of the unit interval to the non-archimedean setting.