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

2011/09/02 by Alina Ostafe, Ostafe, Alina, Igor Shparlinski +1
Mathematics · #11T06 #37P05 #37P25 #65C10 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11T06 #msc:37P05 #msc:37P25 #msc:65C10

paper · pdf · doi:10.48550/arxiv.1109.0575

arxiv created 2011/09/02 · arxiv updated 2011/09/06

Abstract

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.

Related

• Reduction of polynomial dynamical systems modulo primes
• Rational Dynamical Systems
• (Relative) dynamical degrees of rational maps over an algebraic closed field
• Rational preimages in families of dynamical systems
• Computing dynamical degrees