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

Abstract

AbstractLet be a semiabelian variety defined over an algebraically closed field , endowed with a rational self‐map . Let and let be a finitely generated subgroup. We show that the set is a union of finitely many arithmetic progressions along with a set of Banach density equal to . In addition, assuming that is regular, we prove that the set must be finite.