Intersections of orbits of self-maps with subgroups in semiabelian varieties

2022/10/06 by Jason P. Bell, Dragos Ghioca, Bell, Jason P. +1
Computer Science · Engineering · Mathematics · #14K12 #37P55 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2210.03152

openalex publication_date 2022/10/06 · openalex created_date 2022/10/11 · openalex updated_date 2026/07/28

Abstract

Let G be a semiabelian variety defined over an algebraically closed field K, endowed with a rational self-map Φ. Let α∈ G(K) and let Γ⊆ G(K) be a finitely generated subgroup. We show that the set \n∈ℕ\colon Φⁿ(α)∈ Γ\ is a union of finitely many arithmetic progressions along with a set of Banach density equal to 0. In addition, assuming Φ is regular, we prove that the set S must be finite.

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