National Tsing Hua University
MATH 6225 - Topics on Dynamical Systems



Instructors: ³¯°ê¼ý Kuo-Chang Chen, Francisco Javier Muñoz Almaraz

Hours and Days: Tuesdays 1:10-3:00PM and Thursdays 1:10-2:00PM

Classroom: ºî¤T 723

Office Hours: T3T4 or By appointments

Contact Information: 33067, ºî¤T 609

Email: kchen(-at-)math.nthu.edu.tw, malmaraz(-at)esi.us.es

Prerequisite: Those who intended to take this course should have some background on ordinary differential equations and real analysis. Apart from that, I will try to make this course as self-contained as possible; no prerequisite knowledge on dynamical systems is required.

References: V.Arnold: Mathematical Methods of Classical Mechanics, Springer-Verlag 1989.
K.Meyer, G. Hall: Introduction to Hamiltonian Systems and the N-body Problem, Springer-Verlag, 1992.

Course Description: This topic course is jointly offered by K.-C.Chen and F.J. Muñoz Almaraz. We will also arrange some speakers to give lectures during regular hours of this course. The main theme of this topic course is Hamiltonian systems, but our invited speakers may or may not lecture on closely related topics. Detailed schedule of talks by invited speakers will be determined later. In the first half of the course (9/16-11/13) I will give an introductory course on Hamiltonian dynamical systems. We will follow closely the third part of V. Arnold's book. Topics to be covered are (tentatively)
  1. Differential forms
  2. Symplectic manifolds
  3. Canonical formalism
  4. Introduction to perturbation theory
  5. Normal forms
The second half of the course offered by Dr. Munoz Almaraz will be more related to his research work on reversible Hamiltonian systems. Details of his lectures will be distributed later. Click HERE for an abstract.

Grading: Written report/homework assignments: 60%
Oral presentation: 40%