Power maps and subvarieties of the complex algebraic n--torus

2008/02/20 by Iskander Aliev, Aliev, Iskander, Chris Smyth +1
Mathematics · #11G35 #14L40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #math.DS #math.NT #msc:11G35 #msc:14L40

paper · pdf · doi:10.48550/arxiv.0802.2938

12 pages, corrected typos

openalex publication_date 2008/02/20 · arxiv created 2008/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a subvariety V of the complex algebraic torus \mathbb G_{\rm m}ⁿ defined by polynomials of total degree at most d and a power map ϕ: \mathbb G_{\rm m}ⁿ → \mathbb G_{\rm m}ⁿ, the points \bf x whose forward orbits \mathcal O_ϕ(\bf x) belong to V form its \em stable subvariety S(V,ϕ). The main result of the paper provides an upper bound T=T(n,d,ϕ) for the number of iterations of the power map ϕ required to ``cut off'' the points of V that do not belong to S.

Citations

• Linear Equations in Variables which Lie in a Multiplicative Group

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