J-Stability in non-archimedean dynamics

2021/02/11 by Benedetto, Robert L., Lee, Junghun
#37P05 (Secondary) #37P40 #37P45 #37P50 (Primary) 11S82 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.05841

Abstract

Let C_v be a complete, algebraically closed non-archimedean field, and let f ∈ C_v(z) be a rational function of degree d ≥ 2. If f satisfies a bounded contraction condition on its Julia set, we prove that small perturbations of f have dynamics conjugate to those of f on their Julia sets.

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