对函数f(x)=(cx+d)/(ax+b)的n次迭代周期性的探讨

Inquiring into the Periodicity of Function ■of nth power

就函数的特征根方程ax2＋（b－c）x－d＝0的判别式△＝0，△＞0，△＜0讨论f[n]（x）＝x的存在性．给出存在n使f[n]（x）＝x成立时，a，b，c，d满足的条件，并给出一些特例及定理的应用．

Discuss the existance of function f[n] (x) = x by the cliscriminant △ = 0, △ > 0, △ < 0 of the eqution ax2 + (b - c)x - d = 0, with a characteristic root of function .Give the terms that satisfy a, b,c,d when n makes f[n] (x) = x tenable and som special instances and applications of certain theorems.