指数函数y=a^x的不动点与轨道的稳定性研究

The Fixed Points and Orbits Stability of Function y=a^x

本文从一个无穷迭代函数的收敛值的谬论出发,讨论了指数函数y=ax的不动点的稳定性,并以Lambert W函数的形式给出了该函数的不动点的解析式。同时文中对该函数的最小周期为2的轨道的稳定性进行了讨论,并且用萨尔可夫斯基定理证明了该函数不可能有最小周期超过2的轨道。

Started from a fallacy on infinite exponential tower,the fixed points stability of function y=a^x are discussed in the paper,and the analytical form of the fixed points is provided by using Lambert W function.The orbits of the function are also classified,and by Sharkovsky’s theorem,it is proved in the paper that there is no orbit with minimal period higher than 2.