2008/07/25 by Thomas Scanlon, Scanlon, Thomas
Mathematics · #11D88 #37F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.AG #math.DS #math.NT #msc:11D88 #msc:37F10
paper · pdf · doi:10.48550/arxiv.0807.4162
arxiv created 2008/07/25 · openalex publication_date 2008/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (K,|⋅|) be a complete discretely valued field and f:\mathbb B1(K,1) → \mathbb B1(K,1) a nonconstant analytic map from the unit back to itself. We assume that 0 is an attracting fixed point of f. Let a ∈ K with limn → ∞ fn(a) = 0 and consider the orbit \mathcal Of(a) := \fn(a) : n ∈ \mathbb N \. We show that if 0 is a superattracting fixed point, then every irreducible analytic subvariety of \mathbb Bn(K,1) meeting \mathcal Of(a)n in an analytically Zariski dense set is defined by equations of the form xi = b and xj = f^ℓ(xk). When 0 is an attracting, non-superattracting point, we show that all analytic relations come from algebraic tori.