On some dynamical systems in finite fields and residue rings
Igor E. Shparlinski · Discrete and Continuous Dynamical Systems · 2007
We use character sums to confirm several recent conjectures ofV. I. Arnold on the uniformity of distribution properties ofa certain dynamical system in a finite field. On the other hand,we show that some conjectures are wrong. We also analyze severalother conjectures ofV. I. Arnold related to the orbit length of similar dynamicalsystems in residue rings and outline possible ways to provethem. We also show that some of them requirefurther tuning.