Proof of a dynamical Bogomolov conjecture for lines under polynomial   actions
  We prove a dynamical version of the Bogomolov conjecture in the special case of lines in affine space A^m under the action of a map (f_1,...,f_m) where each f_i is a polynomial in Q-bar[X] of the same degree. 
Dragos Ghioca and Thomas J. Tucker