Differentiable Dynamical Systems. Introduction to Chaos

Lectures: Montag, 13:15 -- 14:45, SG 3-13

Tutorial: (every second) Donnerstag, 15:15 -- 16:45, SG 3-13

Dynamical systems are concerned with evolutionary processes. Some examples of dynamical systems are 

celestial mechanics and population dynamics. One of the most remarkable phenomenon is possibility of 

deterministic chaos: differences in initial conditions (such as those due to rounding errors in numerical computation) 

yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. 

In this course we study basic properties of chaotic dynamical systems. 

All necessarily notions will be introduced during the course. 

Previous knowledge of dynamical systems is not assumed.

Topics:

• Symbolic dynamics, Smale's horseshoe. 

• Equivalence relations, conjugacy.

• Hyperbolic points and sets.

• Stable and unstable manifolds.

• Structural Stability and shadowing.

Books:

• Pilyugin, Sergei. Spaces of dynamical systems. De Gruyter, Berlin, 2012. 

• Hasselblatt, Boris; Katok, Anatole. A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. 

• Brin, Michael; Stuck, Garrett. Introduction to dynamical systems. Cambridge, 2002.

• 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.

Exercises:

1. Excercise 1

2. Excercise 2

3. Excercise 3

4. Excercise 4

5. Excercise 5

6. Excercise 6

7. Excercise 7

   1. Excercise 8 was not given

8. Excercise 9