Chaotische Dynamical Systems

COURSE OBJECTIVE
After this course, the student

• has a basic knowledge of nonlinear dynamical systems.
• understands the mechanisms that cause chaos in 1-dimensional maps and is able to investigate these maps.
• understands mechanisms that cause chaos in 2-dimensional maps and is able to apply techniques to investigate these maps.
• is able to compute and recognize important nonlinear bifurcations and appreciates their importance for dynamics.
• has used the theory of dynamical systems in an application, and has communicated his experience to his/her peers.

COURSE CONTENT
Modern dynamical systems theory originates with the work of Poincare, who revolutionized the study of dynamical systems by introducing qualitative techniques of geometry and topology to discuss global properties of solutions. The study of chaotic dynamical systems from the 1960s on lead to a breakthrough in science and an explosion of interest in the field of dynamical systems.

This course investigates nonlinear dynamical systems and explains basic ideas of the field in low dimensional settings of iterated maps on the line and in the plane. Important results and ideas are explained in this context, such as symbolic dynamics, "period three implies chaos", period doubling route to chaos, the Smale horseshoe map and bifurcations of periodic points.

TEACHING METHODS
Lectures, tutorials and a group project

TYPE OF ASSESSMENT
Exams and a group project