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We introduce and study algebraic dynamical systems generated by triangularsystems of rational functions. We obtain several results about the degreegrowth and linear independence of iterates as well as about possible lengths oftrajectories generated by such dynamical systems over finite fields. Some ofthese results are generalisations of those known in the polynomial case, someare new even in this case.

Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems