Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/195847
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Degree growth, linear independence and periods of a class of rational dynamical systems
Arithmetic, Geometry, Cryptography and Coding Theory : International Conference (13th : 2011) (14 - 18 March 2011 : CIRM, Marseilles, France)
Aubry, Yves; Ritzenthaler, Christophe and Zykin, Alexey. Arithmetic, geometry, cryptography and coding theory : 13th Conference [on] Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, Marseille, France, March 14-18, 2011 : Geocrypt 2011, Bastia, France, June 19-24, 2011, p.131-143
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.