Degree Growth, Linear Independence and Periods of a Class of Rational   Dynamical Systems
  We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of trajectories generated by such dynamical systems over finite fields. Some of these results are generalisations of those known in the polynomial case, some are new even in this case. 
Alina Ostafe and Igor Shparlinski
math.NT math.DS