Quasi-Linear Type Iterative Equations And Problems Of Degree-Preservation In Iteration

Iteration is one of the most important topic in nonlinear science. Iteration of a continuous map defines a discrete dynamical system. In Chapter l,we in-troduces self mappings on an interval, the roots of the functions, functional equations and the embedding flow. Some basic concepts and results are stated.In Chapter 2, a kind of quasi-linear iterative equations has been discussed. Existence, uniqueness and stability of the continuous solutions of the equation are proved by using fixed point theorem.In Chapter 3, the degree-preserving polynomials on R² are discussed. With aid of computer algebraic systems, conditions are given to classify polynomials which are degree-preserved.In Chapter 4, the dynamical system in continued fractions, modeled by iteration, and related results on periodicity and chaos are summarized.