有限域上的一维单项动力系统
Monomial Dynamical Systems of Dimension One over Finite Fields
摘要：
本文从算术和图论的观点研究了有限域上的一维单项动力系统。给出了周期为r的周期点和长度为r的圈的个数公式。然后我们计算周期点和圈的自然分布。定义并计算了周期点和圈的Dirichlet分布。特别地，我们将单项动力系统与函数场结合起来计算分布。
英文摘要：
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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