The Research On The Iterative Expression And Iteration Root

In recent years, along with the progress of science and engineering, theory of iteration and iterative roots is also developed continually. Iteration is not only an universal phenomenon in nature and human life, but also a subject on dynamic systems. Its results on chaos bring again a tremendous impact to the whole knowledge system of human beings, after principle of relativity and quantum mechanics. Iterative equations are those equations which involve iteration as a basic operation and closely link with dynamical systems, affect the development of natural science and engineering deeply. The problem of Iterative expression and Iteration root is the most fundamental. In this paper we study the Iterative expression and Iteration root.In chapter one, we introduce the research significance, present situation of Iterative expression and Iteration root , and the arrangement of this paper.In chapter two, First, some preliminary notes are given. Then, the definition, notes, relative properties on Iterative expression, periodic point and Iteration root are instructed in detail.In chapter three, firstly we study the iterative expression: generalize the main methods for calculating the iterative expression; propose the iterative expression for some functions; the application of babbage equation;Give the comprehension for periodic points. And then study the Iteration root of polynomial function.In chapter four, at first we summarize the results, analyze the problems in this paper, then show the direction of research.