Record: Yes

Level: Graduate

Language: Chinese

Prerequisite

Abstract

This course is a continuation of last semester and will cover the following topics:

1)  Normal forms of Hamiltonian systems and bifurcation theory;

2)  Averaging methods of classical perturbation theory;

3)  KAM stability of Hamiltonian systems;

4)  Effective stability of nearly integrable systems;

5)  Numerical stability of symplectic geometric methods.

Reference

1.   V. I. Arnold, Mathematical Methods of Classical Mechanics (Appendix 1-8 and relevant references up to date), Springer-Verlag New York, 1978.

2.   K. Feng and M. Z. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Zhejiang Science and Technology Press Hangzhou and Springer-Verlag Berlin, 2010.

3.   E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration ---Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag Berlin, 2002.

Syllabus

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.

Lecturer Email: zaijiu@math.ac.cn

TA: Dr. Wei He, hewei@bimsa.cn