Ruelle's zeta function for non-Archimedean rational maps

2025/08/26 by Jiang, Yunping, Wu, Chenxi
#11S82 #37D35 #37P05 #37P10 #37P20 #37P40 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.19374

Abstract

We studied the transfer operators defined over ℂ_p-valued analytic functions for subhyperbolic rational maps on ℚ_p, and showed that the corresponding Ruelle's zeta functions are meromorphic on ℂ_p. We also used ℝ-valued transfer operators to study the shape of the corresponding Julia sets, and proved a Levin-Sodin-Yuditski type identity for general rational maps on ℂ_p. In all the results above, ℚ_p can be replaced with any non-Archimedean local field with characteristic 0, and ℂ_p the metric completion of its algebraic closure.

Citations

• Zeta function and entropy for non-archimedean subhyperbolic dynamics

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