In the winter term 2022/23, I will teach a course

Dynamical Systems

(with exercises). The course will comprise four hours lectures and two hours tutorials per week.

The first half of the course will discuss invariant manifolds and normal forms at stationary points. The second half will be concerned with singular perturbation theory in form of so-called slow-fast systems which evolve on different time scales. Such systems appear frequently in applications, in particular in biology. I assume that participants have already basic knowledge about ordinary differential equations like the fundamental existence and uniqueness theorem of Picard-Lindelöf.

Literature:

• L. Perko: Differential Equations and Dynamical Systems, Springer
• F. Verhulst: Methods and Applications of Singular Perturbations, Springer
• S. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer

Time/Location: Thursday 15:00-17:00 HPS 0282, Friday 13:00-15:00, HPS 1409
Begin: October 20th

Exercises

The tutorials will be organised by Matthias Seiß.