论文标题
在地图的迭代中
On the iterations of the maps $ax^{2^k}+b$ and $(a x^{2^k} + b)^{-1}$ over finite fields of characteristic two
论文作者
论文摘要
图$ x \ mapsto ax^{2^k}+b $在特征两个的有限字段上定义的可能与二进制超级椭圆曲线的重复图有关。依靠此类曲线的一组理性点的结构，我们可以描述地图的可能循环长度。然后，我们将调查扩展到地图$ x \ mapsto（ax^{2^k}+b）^{ - 1} $。我们还注意到这些后一个地图与多项式之间的某些关系$ x^{2^k +1} +x +a $，这些$已在文献中进行了广泛研究。
The maps $x \mapsto ax^{2^k}+b$ defined over finite fields of characteristic two can be related to the duplication map over binary supersingular elliptic curves. Relying upon the structure of the group of rational points of such curves we can describe the possible cycle lengths of the maps. Then we extend our investigation to the maps $x \mapsto (ax^{2^k}+b)^{-1}$. We also notice some relations between these latter maps and the polynomials $x^{2^k+1} + x +a$, which have been extensively studied in literature.
