Analytic Theory Of Iterative Functional Equations

The purpose of dynamical system theory is to study rules of change in state which depends on time. Usually there are two basic forms of dynamical systems: continuous dynamical systems described by differential equations and discrete dynamical systems described by iteration of mappings. Many mathematical models in physics, mechanics, biology and astronomy are given in such forms. Many problems of dynamical systems can be reduced to an iterative functional equations Through years of development, iterative functional equations have become a branch of modern mathematics that are closely related to differential equations, difference equations, integral equations and dynamical systems, playing an important role in the study of experimental science and engineering. Since mathematicians like Babbage, Abel etc., iterative functional equations have formed a theory system with the development of iterative theory. In the introduction part of the thesis,the characteristics and applications of functional iteration, the concepts of iterations and dynamical systems, the concepts of discrete dynamical systems and continuous dynamical systems, the basic forms of iterative equations and the problems of iterative roots and invariant curves and Davie lemma are introduced. A brief introduction is also given about the achievements made in the field of iterative functional equations in recent years.As an important model abstracted from the real world, iterative functional equations are of wide operation significance and application background, being always concerned by mathematicians. In experiment, the analysis of the regulation of system sport is always carried out by means of the records made...