## Math 435: Dynamical Systems

**Course Description**:

This is an introductory course on dynamical systems, aimed at advanced undergraduate students and beginning graduate students. We will mainly study discrete-time dynamical systems, that is, the iteration of maps. A progression of examples will be used to present the concepts and tools for describing asymptotic behavior in dynamical systems. These examples will then be embedded in the general theory and we will also touch upon some recent developments in the field. Several recommended texts are listed below; our main source will be the text by Hasselblatt and Katok. The formal prerequisites for this course, as described in the Rice University Course Catalog, are Math 211 and (CAAM 335 or Math 355) and (CAAM 401 or Math 321). Put differently, familiarity with analysis and linear algebra will be assumed and prior exposure to ordinary differential equations will be useful.

Meeting Time: MWF 2:00 PM -- 2:50 PM

Location: Herman Brown Hall (Room 453)

Website: http://www.ruf.rice.edu/~dtd3/Ma435_Fall09

**Instructor**:

David Damanik

Email: [my last name] at rice dot edu

Phone: x3273

Office: Herman Brown 434

Office Hour: M 3:00 PM -- 4:00 PM and by appointment

**Recommended Texts**:

M. Brin and G. Stuck, *Introduction to Dynamical Systems*, Cambridge University Press, Cambridge, 2002.

R. Devaney, *An Introduction to Chaotic Dynamical Systems*, Second Edition, Westview Press, Boulder, 2003.

B. Hasselblatt and A. Katok, *A First Course in Dynamics - With a Panorama of Recent Developments*, Cambridge University Press, New York, 2003.

**Grades**:

The final grade for the course will be based on your homework scores.

**Homework**:

There will be weekly homework assignments with due date indicated on each problem set. These assignments will be accessible through OWL-Space. The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However, each student is responsible for the final preparation of his or her own homework papers.

**Disabilities Statement**:

If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Allen Center.