On Some Dynamical Systems in Finite Fields and Residue Rings

Details On Some Dynamical Systems in Finite Fields and Residue Rings On Some Dynamical Systems in Finite Fields and Residue Rings

2006-07-30

arxiv.org/abs/math/0607779v3

Discr. and Cont. Dyn. Syst., Ser.A, 2007, v.17, 901-917

Mathematics

Number Theory

Scientific paper

We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show that some conjectures are wrong. We also analyze several other conjectures of V. I. Arnold related to the orbit length of similar dynamical systems in residue rings and outline possible ways to prove them. We also show that some of them require further tuning.

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