Smooth Dynamical Systems

Dynamical systems are concerned with evolutionary processes. Some examples of dynamical systems are celestian mechanics and population dynamics. In this course we study basic properties of smooth dynamical systems, mostly related to the longtime behaviour. The course is based only on basic notions and should be understandable for Bachelor students.

The following topics will be covered in the course:

1. Cascades and flows.
2. Fixed points, periodic points.
3. Symbolic dynamics, Smale's horseshoe.
4. Equivalence relations, conjugacy.
5. Hyperbolic points and sets.
6. Stable and unstable manifolds.
7. Structural Stability and shadowing.

References

• Pilyugin, Sergei. Spaces of dynamical systems. De Gruyter, Berlin, 2012.
• Katok, Anatole; Hasselblatt, Boris. Introduction to the modern theory of dynamical systems. Cambridge, 1995.
• Brin, Michael; Stuck, Garrett. Introduction to dynamical systems. Cambridge, 2002.

Date and time info
Tuesday 11.15 - 12.45 (lectures), Wednesday 13.15 - 14.45 (exercises)

Keywords
Dynamical system, fixed point, hyperbolicity, structural stability, invariant manifold

Audience
MSc students, PhD students, Postdocs

Language
English