Differentiable Dynamicas Systems I

Lectures: Mittwoch 9:15 -- 10:45, P-701

Tutorial: (every second) Donnerstags 11:15 -- 12:45, A-314

Dynamical systems are concerned with evolutionary processes. Some examples of dynamical systems are celestial mechanics and population dynamics. In this course we study basic properties of smooth dynamical systems, mostly related to the long-time behavior. In the first part of the course we consider dynamical systems, which behavior can be relatively easy described.

The following topics will be covered in the course:

1. Topological and differential equivalence.

2. Lyapunov functions.

3. Local bifurcations.

Books:

1. Hasselblatt, B.; Katok, A. A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. x+424 pp. 

2. Katok, A.; Hasselblatt, B. Introduction to the modern theory of dynamical systems. Cambridge, 1995.

3. Guckenheimer, J.; Holmes, P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, 1983.

4. Broer, H. W.; Dumortier, F.; van Strien, S. J.; Takens, F. Structures in dynamics. Finite-dimensional deterministic studies. Studies in Mathematical Physics, 2. North-Holland Publishing Co., Amsterdam, 1991.

There is a seminar "Dynamical Systems" on Wednesday at 2pm. Please contact Ilona Kosiuk to be added to a mail list.

Excercises

1. Excercises 1

2. Excercises 2

3. Excercises 3

4. Excercises 4

5. Excercises 5

6. Excercises 6

7. Excercises 7

8. Excercises 8

   1. There is no Excercise 9.

9. Excercises 10

Detailed Program