A non-archimedean λ-lemma

2017/12/04 by Thomas Silverman, Silverman, Thomas · 1 citation
Mathematics · #37P50 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1712.01372

openalex publication_date 2017/12/04 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We provide a framework for studying the dynamics of families of one-variable rational functions parametrized by Berkovich spaces over a complete non-archimedean field. We prove a non-archimedean analogue of Mañé, Sad, and Sullivan's λ-Lemma and use this to show an equivalence of two stability conditions for families of rational functions parametrized by an open subset of the Berkovich affine line.

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