p-adic rational maps having empty Fatou set

2024/01/12 by Aihua Fan, Shilei Fan, Fan, Aihua +5
Computer Science · Mathematics · #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37P05 #Secondary 11S82 #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2401.06314

openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On any finite algebraic extension K of the field \Q_p of p-adic numbers, there exist rational maps ϕ∈ K(z) such that dynamical system (ℙ¹(K),ϕ) has empty Fatou set, i.e. the iteration family \ϕⁿ: n≥ 0\ is nowhere equicontinuous.

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