变分和上同调的差分离散形式及其应用

Variation,Discrete Difference form of Cohomology and Their Application

回顾经典力学中的变分原理和离散变分原理的基本内容;简单介绍相空间作为辛流形上的欧拉-拉格朗日上同调、辛结构守恒的充要条件和刘维定理及其推广.在此基础上,介绍差分离散变分原理和欧拉-拉格朗日上同调的差分离散形式的概念和方法;及其在辛算法等领域的一些简单应用.

Based upon review of variation principle, Euler-Lagrange cohomology, conservation of symplectic structure and Liouville theory in classical mechanics, then we mainly introduce the discrete difference version and method of variation principle, Euler-Lagrange cohomology, conservation of symplectic structure and Liouville theory as well as some applications.