二次多项式映射的3-周期点判定

Discrimination of the 3-periodic points of a quadratic polynomial

作者通过对实系数多项式在复数域上的分解,给出了一般非线性多项式的3-周期点的等价命题,利用这一等价命题,借助多项式的完全判别系统,作者给出一般二次映射3-周期点存在性的充要条件。

A equivalent proposition for the determination of the 3- periodic points of a real coefficient polynomial is provided by decomposing it in complex field. By this equivalent proposition, a necessary and sufficient condition of determination 3-periodic points of a quadratic polynomial is obtained, based on a complete discrimination system.