The Research On The Iterative Problems Of Several Types Of Functions

In recent years, as the human nature science and technology grow with each passing day, especially the rapid development of the electronic computer technology,the iteration and a series of theories related to the iteration also make a spurt of progress. The iteration has abundant practical background, it widely exists in nature and is closely related to human life. More importantly, the iteration also has profound mathematical foundation, it produces the dynamic system, is the basis of the dynamic system, and also is the main content of the dynamic system’s research.While,the functional iteration expression and the cycle problem of function iterative is one of the most fundamental problem in iteration theory. In this paper, we will try to study the iterative expression and iteration cycle and periodic point of several kinds of special function.In chapter one,we will introduce the writing background of this article and the research status of the function iteration expression and iteration cycle simply, and present the main content of this paper briefly.In chapter two, mainly though the conjugated similarly method and recursive method to discuss the iterative expression of several kinds of special function.In chapter three, mainly to discuss several kinds of special and interesting methods which are used to calculate the iterative expression of several types of fractional function.In chapter four, on the basis of the second and third chapter, through the famous Babbage equation namely the function equationf~n(x) =x and function iterative expressions to explore the iterative cycle and periodic point of several kinds of function.