Abstract. We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell-Lang conjecture. 1.

Abstract. We define the Mordell exceptional locus Z(V) for affine varieties V ⊂ G g a with respect to the action of a product of Drinfeld modules on the coordinates of G g a. We show that Z(V) is a closed subset of V. We also show that there are finitely many maximal algebraic φ-modules whose translates lie in V. Our results are motivated by Denis-Mordell-Lang conjecture for Drinfeld modules. 1.