Instructor: Pawel Gora
Office: LB-901-17, tel. 848-2424, ext. 3257,
e-mail: pgora@mathstat.concordia.ca
Office hours: Tuesdays: 1:30--2:30
Wednesdays: 10:15--11:30
Thursdays: 1:30--2:30
or by appointment.
Recommended Textbooks:
1) Petersen, Karl, Ergodic theory. Corrected reprint of the 1983 original. Cambridge Studies in Advanced Mathematics, 2. Cambridge University Press, Cambridge, 1989.
2) Boyarsky, Abraham; Góra, Paweł, Laws of chaos, Invariant measures and dynamical systems in one dimension. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1997.
3) "Fractals Everywhere" by Michael F.Barnsley
Topics:
1. Introduction to Ergodic Theory
2. Basic Constructions in Ergodic Theory
3. Ergodic Theorems
4. Frobenius-Perron operator and absolutely continuous invariant measures
5. Metric spaces, Hausdorff metric. Iterated Function Systems and their attractors.
Computer graphics using IFS attractors. Fractal dimension.
Additional topics may be covered if time permits.
Assignments:
Homework will be given weekly and constitutes a very important part of the course. Students are encouraged to use Maple (or other such system) whenever it is applicable. Late homework will not be accepted.
Midterm Exam: There will be an in-class test. The exact date of the exam is Thursday , November 3rd.
Final Exam: 3 hours at the end of the semester.
Evaluation: The final mark is the maximum of :
20% assignments + 20% midterm test + 60% final exam
100% final exam