The Julia Set Of Random Dynamical System

Earlier in 1900s P.Fatou and G.Julia indepently developed iteration theory of a complex function, from then on, the thoery of the dynamics system of complex function has developed about one hundred years. Recently, Random dynamical system is an important part of this subject. Now studying of random dynamical system has two direction: Studying the iteration of a serial and studying the iteration of all serials.Chapter one of this paper discuss the random dynamical system formed by limited rational functions. Some necessary conditions and some sufficient conditions are give for the Julia set to have interior points. Additional, for any positive number L, it proved that it is easy to construct a set of polynomial, whose Julia set have points but is not the whole plane, however, the distances of one another of the classical Julia sets of them is greater then L. This phenomenon isn't exists in the random dynamical system constructed by two polynomial.Chapter two study iteration of a serial of polynomial, discussed the sufficient and necessary conditions and denseness of the Julia set, the relative random dynamical system is constructed by some high degree polynomial. In addition, it discuss the Mandelbrot set of a kind of polynomial.