The Investigation on the Similarities of the M-J Set of the Rational Functions with One Parameter

A group general Mandelbrot and Julia sets of the rational functions with one parameter constructed by Newton’s method are discussed.The relation about the group similarities between the general Mandelbrot sets and Julia sets,and the common Mandelbrot sets and Julia sets of zn +c(n ∈ Z,n≥2) are investigated.It is found that their group similarities between these Mandelbrot sets and these Julia sets are very analogous.This result can be explained that the dynamics on the complex plane have the intimate connection with the dynamics on the parameters plane,so this connection has universality.It gives a new way to improve the theory of the Mandelbrot sets and the Julia sets.