國立清華大學數學系
動態系統專題
Math 6225-00 (Fall 2012) Topics on Dynamical Systems

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Instructor: 陳國璋 Kuo-Chang Chen Hours and days: F5F6F7 Classroom: 綜三 727 Prerequisite: 實變函數論、常微分方程

Office: 綜三 609 Phone Number: (03) 5715131 Ext: 33067 Office Hours: By appointments Email: kchen@math.nthu.edu.tw

Course Description:

This is a research oriented course intended for graduate students who are interested in dynamical systems and analysis. It consists of short courses on various topics which are of significant interests but not always covered in standard courses of dynamical systems, differential equations, or analysis. Basic concepts and examples will be introduced, and further readings will be assigned in classes. Students are expected to master themselves in at least one of the selected topics, and prepare a survey paper and a formal presentation by the end of the semester.

Topics to be covered include:

1. Morse theory

2. Conley index theory

3. Method of symbolic computation

4. KAM theory

5. Circle maps and twist maps

6. Aubry-Mather theory

Those who wish to take this course should have some background knowledge on real analysis, ordinary differential equations, and topology.

Grading:

Final paper (50%) and oral presentation (50%)

Attendance

Students are expected to attend every scheduled class. It is the student's responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.