國立清華大學數學系

遍歷理論

Math 6210-00 (Spring 2021) Ergodic Theory 

Course Description:

Ergodic theory was motivated by problems in statistical physics, and has developed into an independent mathematical subject. It concerns long time average of typical orbits of measurable dynamical systems, and has far-reaching connections with other mathematical subjects, such as functional analysis, number theory, probability, differential geometry, among others. This course is intended for graduate and advanced undergraduate students who are interested in dynamical systems and analysis. Prerequisite knowledge include real analysis and differential equations (undergraduate level). Basic concepts and examples will be introduced, and further readings will be assigned in classes. Topics to be covered include:

1. Measure preserving systems

2. Invariant and ergodic measures

3. Ergodic theorems

4. Recurrence in dynamical systems

5. Entropy

Registered students are recommended to use the iLMS e-learning system (http://www.nthu.edu.tw/elearning.php), where updates of the course will be posted.  

Textbook/References: 

[1] 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)

[2] K.E. Peterson: Ergodic Theory, Cambridge University Press, 1983.

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

Grading:

Homework assignments: 60%. (posted on iLMS e-learning system)

Final project: 40%