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arXiv · 2210.03152

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

Jason P. Bell·Dragos Ghioca
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Abstract

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $Φ$. Let $α\in G(K)$ and let $Γ\subseteq G(K)$ be a finitely generated subgroup. We show that the set $\{n\in\mathbb{N}\colon Φ^n(α)\in Γ\}$ 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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Jason P. Bell, Dragos Ghioca. 2022-10-06. Intersections of orbits of self-maps with subgroups in semiabelian varieties. https://arxiv.org/abs/2210.03152

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