论文标题
多项式图的动力学在有限场上
Dynamics of polynomial maps over finite fields
论文作者
论文摘要
令$ \ mathbb {f} _q $为有$ q $元素的有限字段，让$ n $为正整数。在本文中，我们研究了与地图$ x \ mapsto x^n h（x^{\ frac {q-1} {m}}}）$相关的图形，其中$ h（x）\ in \ in \ mathbb {f} _q [x]。特别是，我们提供了与单次图相关的功能图。由于我们的结果，提供了这些类别地图的连接组件的数量，周期的长度和固定点的数量。
Let $\mathbb{F}_q$ be a finite field with $q$ elements and let $n$ be a positive integer. In this paper, we study the digraph associated to the map $x\mapsto x^n h(x^{\frac{q-1}{m}})$, where $h(x)\in\mathbb{F}_q[x].$ We completely determine the associated functional graph of maps that satisfy a certain condition of regularity. In particular, we provide the functional graphs associated to monomial maps. As a consequence of our results, the number of connected components, length of the cycles and number of fixed points of these class of maps are provided.
