Symplectic Structure Of The Difference Discrete Variational

In this article,I will introduce the concepts in Mathematics and Physics related to symplectic structure;then give a easy proof of which the Hamilton phase flow always conserves the symplectic structure;then introduce two different theory based on exponential map method or difference discrete variation method to generate numerical symplectic conserving schemes;then explain the relationship between symplectic structure conserving schemes and first integrals;and at the end I will give the results of my numerical experiments.