Topological Space Problem For Some Classes Of Iterated Function

In the 1880s,the research of dynamic system had been originated with a French mathematicians H.Poincare,who published continuously papers Differential Equation To DetermineCurve. Iteration and Iterative roots is the important component of dynamic system, also is the old problem. About one hundred years ago, C.Babbage, Abel, Schroder began to study Iteration and Iterative roots of Map. In recent years, Along with the development of natural science and technology, Iteration and Iterative roots is also developing constantly,which influences the development of natural science.In chapter one, we introduce simply the development about dynamical system and the background of this paper.In chapter two, we introduce some basic definitions of iteration, and we introduce the progress of the iteration of a function, quadratic function, high function and linear fractional function. On the basis of these,we give the the iteration of special quadratic function, high function and linear fractional function. Recursion is also introduced some of the basic theory and application.In chapter three, we introduce an iterative root, some of the basic theory of iterative equations, introduces the monotone function, piecewise monotone function iteration progress of the root, and quadratic polynomial equation and the general polynomial equation of some properties .In chapter four, first we summarize the results in this thesis, then we analyze the questions that exist in this studying and show the direction of studying that we will do in future.