On some dynamical systems in finite fields and residue rings

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)901-917
Number of pages17
JournalDiscrete and Continuous Dynamical Systems
Volume17
Issue number4
Publication statusPublished - Apr 2007

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