Prime divisors in polynomial orbits over function fields

Abstract

Given a polynomial $\varphi$ over a global function field $K$ and a wandering base point $b\in K$, we give a geometric condition on $\varphi$ ensuring the existence of primitive prime divisors for almost all points in the orbit ${\mathcal{O}}_{\varphi }(b):=\{{\varphi }^n(b){\}}_{n\ge 0}$