Arnold变换的周期及其应用

On the Periods of Arnold Transformations and Some Applications

探讨了Arnold变换的周期性,主要结果包括:①通过构造一个整数序列{Gn}并研究Arnold变换的周期与该整数序列{Gn}的联系,获得了一些关于Arnold变换周期的新的性质,特别是文中得到的素数阶数字图像周期的上界比已有的结果更精确;②给出了计算Arnold变换最小周期的一种算法,实验结果说明该算法优于已有的一些算法。

The properties of the period of Arnold transformation are studied. The main results include:① A new integer sequence is introduced, then by making use of the properties of this sequence some new properties of the periods of Arnold transformation are obtained, especially in the prime situation ,a more accurate upper bound of the periods is given; ② A new algorithm is proposed which is better than that proposed by some other papers.