Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms

Abstract

We prove that for a dynamical system on an algebraic variety over $\overline{\mathbb{Q}}$ generated by finitely many unramified endomorphisms, it is decidable whether a given point has a finite orbit. This is achieved by establishing an effective upper bound for the size of finite orbits in integral algebraic dynamical systems with unramified morphisms.