Monomial Dynamical Systems of Dimension One over Finite Fields

Details Monomial Dynamical Systems of Dimension One over Finite Fields Monomial Dynamical Systems of Dimension One over Finite Fields

2009-10-29

arxiv.org/abs/0910.5550v5

Mathematics

Number Theory

Accepted by Acta Arithmetica. (SCI)

Scientific paper

In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we compute the natural distributions of periodic points and cycles. We also define and compute the Dirichlet distributions of periodic points and cycles. Especially, we associate the monomial dynamical systems with function fields to compute distributions.

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