國立清華大學數學系
遍歷理論 (簡介)
Math 6210-00 (Spring 2013) Ergodic Theory (an introduction)

---

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

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

Course Description:

Ergodic theory was motivated by problems in statistical physics, and is now an important mathematical subject which studies dynamical systems with invariant measures. It concerns long time behavior and average of measurable dynamical systems, and has far-reaching connections with other subjects, such as functional analysis, number theory, probability, differential geometry, among others. This course is intended for graduate students who are interested in dynamical systems and analysis. Basic concepts and examples will be introduced, and further readings will be assigned in classes.

Topics to be covered include:

1. Recurrence in dynamical systems

2. Invariant and ergodic measures

3. Ergodic theorems

4. Measure theoretic entropy

Primary References:

1. K.E. Peterson, Ergodic Theory, Cambridge University Press, 1983.

2. M. Pollicott and M. Yuri: Dynamical Systems and Ergodic Theory, London Mathematical Society, Cambridge University Press, 1998.
Available at http://www.warwick.ac.uk/~masdbl/book.html

3. P.Walters: An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Springer-Verlag, 1982.

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.