论文标题
自图的轨道与Semiabelian品种中亚组的轨道交叉点
Intersections of orbits of self-maps with subgroups in semiabelian varieties
论文作者
论文摘要
让$ g $为在代数封闭的$ k $上定义的半近婚夫品种，并具有理性的自动图$φ$。令$α\在g（k）$中，让$γ\ subseteq g（k）$为有限生成的子组。我们表明，集合$ \ {n \ in \ mathbb {n} \colonφ^n（α）\ inγ\} $是有限的许多算术进程的结合，以及一组Banach密度，等于$ 0 $。此外，假设$φ$是常规的，我们证明了集合$ S $必须是有限的。
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.
