Symplectic Geometric Method of Hamiltoian Systems
本课程在概括介绍哈密尔顿系统基本理论的基础上，主要讲授辛几何算法的基本知识，介绍其前沿进展，内容包括：哈密尔顿系统概论、数值积分方法概论、辛几何算法、KAM理论、向后误差分析、辛算法的稳定性、若干应用.
Lecturer
Date
14th September ~ 9th December, 2021
Prerequisite
数学与应用数学专业本科知识；微分流形、外微分形式、辛几何初步
Reference
1. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag Berlin, 1978.
2. E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration---Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag, 2002.
3. K. Feng, M. Z. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Zhejiang Science and Technology Publishing House, Hangzhou and Springer-Verlag Berlin, 2010.
2. E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration---Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag, 2002.
3. K. Feng, M. Z. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Zhejiang Science and Technology Publishing House, Hangzhou and Springer-Verlag Berlin, 2010.
Video Public
No
Notes Public
No
Lecturer Intro
Zaijiu Shang is a Professor of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and a Post Teacher at the University of Chinese Academy of Sciences (2015-). He was the deputy director (2003-2011) and the director (2012-2016) of the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He has been served as a member of editorial boards of Acta Math. Appl. Sinica (2007-), Acta Math. Sinica (2009-), Science China: Mathematics (2013-), and Applied Mathematics (HUST 2013-). He is working in the fields of dynamical systems and geometrical numerical methods. He won the second prize in “the Science and Technology Progress Award of the State Education Commission (1993)”. He was one of the core members of the project “Symplectic Geometric Algorithms of Hamiltonian Systems” which won the first prize of the National Natural Science Awards (Kang Feng etc., 1997), and his representative achievements include stability theory of symplectic algorithms and volume-preserving algorithms for source-free systems.