The Application of Ergodic Sequence to Quantitative Theory of Averaging Methods in Dynamical System

In this paper,we mainly study the ergodic sequence and its application.Based on the ergodic functions,we first introduce the definition of ergodic sequence.Then we investigate the ergodic problem in two directions and get some properties of ergodic sequence.Finally we give some quantitative properties of solutions of discrete dynamical system by means of averaging methods.