This course is intended to be a first course to both dynamical systems and ergodic theory. We aim to give a direct and detailed introduction to the basic theory. The course will be divided into three parts. In the first part , we concentrate on topological dynamics. The second part deals with ergodic theory and measurable dynamics. The third part consists of more advanced material of thermodynamic formalism.
This course aims for both advanced bachelor students and master students in Mathematics. As prerequisites, student are expected to have some familiarities with analysis and basic linear algebra. In addiction, some basic understanding of point set topology and measure theory is also necessary.
The lecture and exercise session are hold in room SR C.
Lecture:
Monday, 16pm to 17:40pm
Friday of every odd week, 14pm to 15:40pm
Exercise Session:
Friday of every even week, 14pm to 15:40pm
Office Hour:
Thursday 16:00pm to 17:00pm.
The location for office hour is room A104, 3rd floor, INF 206
There will be an oral final exam at the end of the course. To be admitted to the exam, the student needs to achieve at least 50% of the points that are graded on the exercise sheets.
The homework (exercise sheet) will be given once two weeks. They will be post here on this webpage at the end of odd weeks. They will be partially graded. To be admitted to the final exam, the student needs to achieve at least 50% of the grading homework.
Pollicott-Yuri, Dynamical Systems and Ergodic Theory
Brin-Stuck, Introduction to Dynamical Systems
Katok-Hasselblatt, Introduction to the Modern Theory of Dynamical Systems
Bowen, Equilibrium States and Ergodic Theory of Anosov Diffeomorphism
Bedford-Keane-Series, Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces.